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1.
Here we prove the following result.
Theorem 1.1.Let X be an integral projective curve of arithmetic genus g and k≧ ≧4 an integer. Assume the existence of L ∈ Pick
(X) with h
0
(X, L)=2 and L spanned. Fix a rank 1 torsion free sheaf M on X with h
0(X,M)=r+1≧2, h1
(X, M)≧2 and M spanned by its global sections. Set d≔deg(M) and s≔max {n≧0:h
0 (X, M ⊗(L*)⊗n)>0}. Then one of the following cases occur:
We find also other upper bounds onh
0 (X, F).
| (a) | M≊L ⊗r; |
| (b) | M is the subsheaf of ω X⊗(L*)⊗t, t:=g−d+r−1, spanned by H0(X, ωX⊗(L*)⊗t); |
| (c) | there is a rank 1 torsion free sheaf F on X with 1≦h 0(X, F)≦k−2 such that M≊L⊗s⊗F. Moreover, if we fix an integer m with 2≦m≦k−2 and assume r#(s+1)k−(ns+n+1) per every 2≦n≦m, we have h0 (X, F)≦k−m−1. |
Sunto In questo lavoro si dimostra il seguente teorema. Teorem 1.1.Sia X una curva proiettiva ridotta e irriducibile di genere aritmetico g e k≥4 un intero. Si supponga l'esistenza di L ε Pick (X) con h 0 (X, L)=2 e L generato. Si fissi un fascio senza torsione di rango uno M su X con h0 (X, M)=r++1≥2, h1 (X, M) ≧2 e M generato dalle sue sezioni globali. Si ponga d≔deg(M) e s≔max{n≧0:h 0(X, M ⊗(L*)⊗n)>0}. Allora si verifica uno dei casi seguenti:相似文献Si ricavano anche altre maggiorazioni suh 0,(X, F).
(a) M≊L ⊗r; (b) M è il sottofascio di ω X⊗(L*)⊗t, t:=g−d+r−1 generato da H0 (X, ωX⊗(L*)⊗t); (c) esiste un fascio senza torsione di rango un F su X con 1≦h 0 (X, F) <=k−2 tale che M ≊L ⊗8 ⊗ F. Inoltre, se si fissa un intero m con 2≦m≦k−2 e si suppone r#(s+1) k−(ns+n+1) per ogni 2≦n≦m, si ottiene h 0 (X, F)≦k−m−1.
2.
A. S. Sivatski 《Journal of Mathematical Sciences》2007,145(1):4823-4830
The main purpose of the paper is to strengthen previous author’s results. Let k be a field of characteristic ≠ 2, n ≥ 2. Suppose
that elements
are linearly independent over ℤ/2ℤ. We construct a field extension K/k and a quaternion algebra D = (u, v) over K such that
In particular, the algebra A provides an example of an indecomposable algebra of index 2n+1 over a field, the u-invariant and the 2-cohomological dimension of which equal 2n+3 and n + 3, respectively. Bibliography: 10 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 338, 2006, pp. 227–241. 相似文献
| (1) | the field K has no proper extension of odd degree |
| (2) | the u-invariant of K equals 4 |
| (3) | the multiquadratic extension is not 4-excellent, and the quadratic form 〈uv,-u,-v, a〉 provides a relevant counterexample |
| (4) | the central division algebra A = D ⊗E (a, t0) ⊗E (b1, t1) ⋯ ⊗E (bn, tn) does not decompose into a tensor product of two nontrivial central simple algebras over E, where E = K ((t0))((t1)) … ((tn)) is the Laurent series field in the variables t0, t1, …, tn |
| (5) | ind A = 2n+1. |
3.
In this paper, we discuss the representation-finite selfinjective artin algebras of classB
n andC
n and obtain the following main results:
For any fieldk, let Λ be a representation-finite selfinjective artin algebras of classB
n orC
n overk.
相似文献
| (a) | We give the configuration ofZB n andZC n. |
| (b) | We show that Λ is standard. |
| (c) | Under the condition ofk being a perfect field, we describe Λ by boundenk-species and show that Λ is a finite covering of the trivial extension of some tilted algebra of typeB n orC n. |
4.
Yuji Kobayashi 《Archiv der Mathematik》2005,85(3):227-232
Let k ≧ 3 be an integer or k = ∞ and let K be a field. There is a recursive family
of finitely presented groups Gn over a fixed finite alphabet with solvable word problem such that
Received: 22 July 2004 相似文献
| (1) | the center of Gn is trivial for every |
| (2) | the dimension d(n) of the center of the group algebra K · Gn over K is either 1 or k, and |
| (3) | it is undecidable given n whether d(n) = 1 or d(n) = k. |
5.
A. I. Pavlov 《Mathematical Notes》2000,68(3):370-377
The main result of this paper is the following theorem. Suppose thatτ(n) = ∑
d|n
l and the arithmetical functionF satisfies the following conditions:
Then there exist constantsA
1,A
2, andA
3 such that for any fixed \g3\s>0 the following relation holds:
. Moreover, if for any primep the inequality \vbf(p)\vb\s<1 holds and the functionF is strongly multiplicative, thenA
1\s>0.
Translated fromMatematicheskie Zametki, Vol. 68, No. 3, pp. 429–438, September, 2000. 相似文献
| 1) | the functionF is multiplicative; |
| 2) | ifF(n) = ∑ d|n f(d), then there exists an α>0 such that the relationf(n)=O(n −α) holds asn→∞. |
6.
We present results on total domination in a partitioned graph G = (V, E). Let γ
t
(G) denote the total dominating number of G. For a partition , k ≥ 2, of V, let γ
t
(G; V
i
) be the cardinality of a smallest subset of V such that every vertex of V
i
has a neighbour in it and define the following
We summarize known bounds on γ
t
(G) and for graphs with all degrees at least δ we derive the following bounds for f
t
(G; k) and g
t
(G; k).
相似文献
| (i) | For δ ≥ 2 and k ≥ 3 we prove f t (G; k) ≤ 11|V|/7 and this inequality is best possible. |
| (ii) | for δ ≥ 3 we prove that f t (G; 2) ≤ (5/4 − 1/372)|V|. That inequality may not be best possible, but we conjecture that f t (G; 2) ≤ 7|V|/6 is. |
| (iii) | for δ ≥ 3 we prove f t (G; k) ≤ 3|V|/2 and this inequality is best possible. |
| (iv) | for δ ≥ 3 the inequality g t (G; k) ≤ 3|V|/4 holds and is best possible. |
7.
We present a new pivot-based algorithm which can be used with minor modification for the enumeration of the facets of the
convex hull of a set of points, or for the enumeration of the vertices of an arrangement or of a convex polyhedron, in arbitrary
dimension. The algorithm has the following properties:
For example, the algorithm finds thev vertices of a polyhedron inR
d defined by a nondegenerate system ofn inequalities (or, dually, thev facets of the convex hull ofn points inR
d, where each facet contains exactlyd given points) in timeO(ndv) andO(nd) space. Thev vertices in a simple arrangement ofn hyperplanes inR
d can be found inO(n
2
dv) time andO(nd) space complexity. The algorithm is based on inverting finite pivot algorithms for linear programming. 相似文献
| (a) | Virtually no additional storage is required beyond the input data. |
| (b) | The output list produced is free of duplicates. |
| (c) | The algorithm is extremely simple, requires no data structures, and handles all degenerate cases. |
| (d) | The running time is output sensitive for nondegenerate inputs. |
| (e) | The algorithm is easy to parallelize efficiently. |
8.
For the Azimi-Hagler spaces more geometric and topological properties are investigated. Any constructed space is denoted by
X
α,p
. We show
相似文献
| (i) | The subspace [(e nk )] generated by a subsequence (e nk ) of (e n ) is complemented. |
| (ii) | The identity operator from X α,p to X α,p when p > q is unbounded. |
| (iii) | Every bounded linear operator on some subspace of X α,p is compact. It is known that if any X α,p is a dual space, then |
| (iv) | duals of X α,1 spaces contain isometric copies of ℓ ∞ and their preduals contain asymptotically isometric copies of c 0. |
| (v) | We investigate the properties of the operators from X α,p spaces to their predual. |
9.
The star unfolding of a convex polytope with respect to a pointx on its surface is obtained by cutting the surface along the shortest paths fromx to every vertex, and flattening the surface on the plane. We establish two main properties of the star unfolding:
These two properties permit conceptual simplification of several algorithms concerned with shortest paths on polytopes, and
sometimes a worst-case complexity improvement as well:
相似文献
| 1. | It does not self-overlap: it is a simple polygon. |
| 2. | The ridge tree in the unfolding, which is the locus of points with more than one shortest path fromx, is precisely the Voronoi diagram of the images ofx, restricted to the unfolding. |
| • | The construction of the ridge tree (in preparation for shortest-path queries, for instance) can be achieved by an especially simpleO(n 2) algorithm. This is no worst-case complexity improvement, but a considerable simplification nonetheless. |
| • | The exact set of all shortest-path “edge sequences” on a polytope can be found by an algorithm considerably simpler than was known previously, with a time improvement of roughly a factor ofn over the old bound ofO(n 7 logn). |
| • | The geodesic diameter of a polygon can be found inO(n 9 logn) time, an improvement of the previous bestO(n 10) algorithm. |
10.
LetK be a class of spaces which are eigher a pseudo-opens-image of a metric space or ak-space having a compact-countable closedk-network. LetK′ be a class of spaces which are either a Fréchet space with a point-countablek-network or a point-G
δ
k-space having a compact-countablek-network. In this paper, we obtain some sufficient and necessary conditions that the products of finitely or countably many
spaces in the classK orK′ are ak-space. The main results are that
Project supported by the Mathematical Tianyuan Foundation of China 相似文献
| Theorem A | If X, Y∈K. Then X x Y is a k-space if and only if (X, Y) has the Tanaka's condition. |
| Theorem B | The following are equivalent: |
| (a) | BF(ω 2)is false. |
| (b) | For each X, Y ∈ K′, X x Y is a k-space if and only if (X,Y) has the Tanaka's condition. |
11.
LetG be a finite nonsolvable group andH a proper subgroup ofG. In this paper we determine the structure ofG ifG satisfies one of the following conditions:
相似文献
| (1) | Every solvable subgroupK(K⊉H) is eitherp-decomposable or a Schmidt group,p being the smallest odd prime factor of |G|. |
| (2) | |G∶H| is divisible by an odd prime and every solvable subgroupK(K⊉H) is either 2′-closed or a Schmidt group. |
| (3) | |G∶H| is even and every solvable subgroupK(K⊉H) is either 2-closed or a Schmidt group. |
12.
Giuseppe Pellegrino 《Rendiconti del Circolo Matematico di Palermo》1998,47(1):141-168
| 1. | Letm be the greatest integer such that . ThenPG(3,q) contains complete caps of sizek=(m+1)(q+1)+ω, with ω=0, 1, 2. | |
| 2. |
PG(3,q),q≥5, contains complete caps of size |
|
| 3. | InPG(3,q) complete caps different from ovaloids have some external planes. |
13.
A graph G is close to regular or more precisely a （d, d ＋ k）-graph, if the degree of each vertex of G is between d and d ＋ k. Let d ≥ 2 be an integer, and let G be a connected bipartite （d, d＋k）-graph with partite sets X and Y such that ｜X｜- ｜Y｜＋1. If G is of order n without an almost perfect matching, then we show in this paper that·n ≥ 6d ＋7 when k = 1,·n ≥ 4d＋ 5 when k = 2,·n ≥ 4d＋3 when k≥3.Examples will demonstrate that the given bounds on the order of G are the best possible. 相似文献
14.
Yōhei Yamasaki 《Graphs and Combinatorics》1989,5(1):275-282
We have generalized the theory of Shannon's games in [10]. In this paper, we treat a game on a graph with an action of elementary abelian group but our decision of the winner is more general. Our theory can be applied for non-negative integersn andr, to the two games on a graph withn + 1 distinguished terminals whose rules are as follows:
Dedicated to Professor Sin Hitotumatu for his 60'th birthday 相似文献
| (1) | the players Short and Cut play alternately to choose an edge, |
| (2) | the former contracts it and the later deletes it |
| (3) | the former if and only if he connects the terminals into at mostn – r + 1 ones. |
15.
A. S. Sivatski 《Israel Journal of Mathematics》2011,186(1):273-284
Let k be a field, char k ≠ 2, p(t) a monic irreducible polynomial over k, and k
p
= k[t]/pk[t] the corresponding residue field. For a regular quadratic form φ over k we investigate the relationship between two conditions:
| (1) |
The form jkp{\varphi _{{k_p}}} is isotropic. 相似文献
16.
Guo Jingmei 《数学学报(英文版)》1989,5(1):27-36
The main result in this paper is the following:
Theorem.Assume that W is a k-connected compact PL n-manifold with boundary, BdW is (k–1)-connected, k1(BdW is 1-connected for k=1), 0h2k, 2n–h>5and there exists a normal block (n-h-1)-bundle vover W, then
17.
F. G. Timmesfeld 《Archiv der Mathematik》2002,79(6):404-407
Let Φ be a root system of typeA
ℓ, ℓ ≧ 2,D
ℓ, ℓ ≧ 4 orE
ℓ, 6 ≧ ℓ ≧ 8 andG a group generated by nonidentity abelian subgroupsA
r,r∈Φ, satisfying:
18.
Qiu Weisheng 《数学学报(英文版)》1994,10(1):49-58
The Multiplier Theorem is a celebrated theorem in the Design theory. The conditionp>λ is crucial to all known proofs of the multiplier theorem. However in all known examples of difference sets μ
p
. is a multiplier for every primep with (p, v)=1 andp‖n. Thus there is the multiplier conjecture: “The multiplier theorem holds without the assumption thatp>λ”. The general form of the multiplier theorem may be viewed as an attempt to partially resolve the multiplier conjecture,
where the assumption “p>λ” is replaced by “n
1>λ”. Since then Newman (1963), Turyn (1964), and McFarland (1970) attempted to partially resolve the multiplier conjecture
(see [7], [8], [9]). This paper will prove the following result using the representation theory of finite groups and the algebraic
number theory: LetG be an abelian group of orderv,v
0 be the exponent ofG, andD be a (v, k, λ)-difference set inG. Ifn=2n
1, then the general form of the multiplier theorem holds without the assumption thatn
1>λ in any of the following cases:
19.
Let (G, τ) be a commutative Hausdorff locally solid lattice group. In this paper we prove the following:
20.
Laurent Bartholdi 《Israel Journal of Mathematics》2006,154(1):93-139
We develop the theory of “branch algebras”, which are infinite-dimensional associative algebras that are isomorphic, up to
taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting on trees.
In particular, for every field
% MathType!End!2!1! we contruct a
% MathType!End!2!1! which
|