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1.
Let G m,n be the class of strategic games with n players, where each player has m≥2 pure strategies. We are interested in the structure of the set of correlated equilibria of games in G m,n when n→∞. As the number of equilibrium constraints grows slower than the number of pure strategy profiles, it might be conjectured that the set of correlated equilibria becomes large. In this paper, we show that (1) the average relative measure of the set of correlated equilibria is smaller than 2−n; and (2) for each 1<c<m, the solution set contains c n correlated equilibria having disjoint supports with a probability going to 1 as n grows large. The proof of the second result hinges on the following inequality: Let c 1, …, c l be independent and symmetric random vectors in R k, lk. Then the probability that the convex hull of c 1, …, c l intersects R k + is greater than or equal to . Received: December 1998/Final version: March 2000  相似文献   

2.
Denote byG(n; m) a graph ofn vertices andm edges. We prove that everyG(n; [n 2/4]+1) contains a circuit ofl edges for every 3 ≦l<c 2 n, also that everyG(n; [n 2/4]+1) contains ak e(u n, un) withu n=[c 1 logn] (for the definition ofk e(u n, un) see the introduction). Finally fort>t 0 everyG(n; [tn 3/2]) contains a circuit of 2l edges for 2≦l<c 3 t 2. This work was done while the author received support from the National Science Foundation, N.S.F. G.88.  相似文献   

3.
It is proved that if the Banach-Mazur distance between ann-dimensional Minkowski spaceB andl 2 n satisfiesd (B 1 l 2 n ) ≧cn (for some constantc>0 and for bign) thenB contains anA(c)-isomorphic copy ofl 1 k (fork ∼ log log logn). In the special cased (B 1 l 2 n ) = √n,B contains an isometric copy ofl 1 k fork ∼ logn.  相似文献   

4.
We consider a variant of Heilbronn’s triangle problem by investigating for a fixed dimension d≥2 and for integers k≥2 with kd distributions of n points in the d-dimensional unit cube [0,1] d , such that the minimum volume of the simplices, which are determined by (k+1) of these n points is as large as possible. Denoting by Δ k,d (n), the supremum of this minimum volume over all distributions of n points in [0,1] d , we show that c k,d ⋅(log n)1/(dk+1)/n k/(dk+1)Δ k,d (n)≤c k,d ′/n k/d for fixed 2≤kd, and, moreover, for odd integers k≥1, we show the upper bound Δ k,d (n)≤c k,d ″/n k/d+(k−1)/(2d(d−1)), where c k,d ,c k,d ′,c k,d ″>0 are constants. A preliminary version of this paper appeared in COCOON ’05.  相似文献   

5.
1Intr0ducti0nLetAden0tethesetofallfunctionsanalyticinA={z:Izl<1}.LetB={W:WEAandIW(z)l51}.Aisalocallyconvexlineaztop0l0gicalspacewithrespecttothetopologyofuniformconvergenceon`c0mpact8ubsetsofA-LetTh(c1,'tc.-1)={p(z):p(z)EA,Rop(z)>0,p(z)=1 clz czzz ' c.-lz"-l 4z" ',wherecl,',cn-1areforedcomplexconstants}.LetTh,.(b,,-..,b,-,)={p(z):P(z)'EAwithReP(z)>Oandp(z)=1 blz ' b.-lz"-l 4z" '-,wherebl,-'-jbu-1areffeedrealconstantsanddkarerealnumbersf0rk=n,n 1,'--}-LetTu(l1,'i'tI.-1)={…  相似文献   

6.
Oleg Pushin 《K-Theory》2004,31(4):307-321
In this short paper we investigate the relation between higher Chern classes and reduced power operations in motivic cohomology. More precisely, we translate the well-known arguments [5] into the context of motivic cohomology and define higher Chern classes cp,q : K p(X) → H2q-p (X,Z(q)) → H2q-p(X, Z/l(q)), where X is a smooth scheme over the base field k, l is a prime number and char(k) ≠ l. The same approach produces the classes for K-theory with coefficients as well. Let further Pi : Hm(X, Z/l(n)) → Hm+2i(l-1) (X, Z/l(n + i(l - 1))) denote the ith reduced power operation in motivic cohomology, constructed in [2]. The main result of the paper looks as follows.  相似文献   

7.
Let T=(V,E) be a free tree in which each vertex has a weight and each edge has a length. Let n=|V|. Given T and parameters k and l, a (k,l)-tree core is a subtree X of T with diameter l, having k leaves, which minimizes the sum of the weighted distances from all vertices in T to X. In this paper, two efficient algorithms are presented for finding a (k,l)-tree core of T. The first algorithm has O(n2) time complexity for the case that each edge has an arbitrary length. The second algorithm has O(lkn) time complexity for the case that the lengths of all edges are 1. The (k,l)-tree core problem has an application in distributed database systems.  相似文献   

8.
We show that for all k ≥ 3, r > l ≥ 2 there exists constant c = c(k, r, l) such that for large enough n there exists a k‐color‐critical r‐uniform hypergraph on less than n vertices, having more than cnl edges, and having no l‐set of vertices occuring in more than one edge. © 2006 Wiley Periodicals, Inc. J Graph Theory 53: 56–74, 2006  相似文献   

9.
Let c(n, q) be the number of connected labeled graphs with n vertices and q ≤ N = (2n ) edges. Let x = q/n and k = q ? n. We determine functions wk ? 1. a(x) and φ(x) such that c(n, q) ? wk(qN)enφ(x)+a(x) uniformly for all n and qn. If ? > 0 is fixed, n→ ∞ and 4q > (1 + ?)n log n, this formula simplifies to c(n, q) ? (Nq) exp(–ne?2q/n). on the other hand, if k = o(n1/2), this formula simplifies to c(n, n + k) ? 1/2 wk (3/π)1/2 (e/12k)k/2nn?(3k?1)/2.  相似文献   

10.
In this paper, we study numerical properties of Chern classes of certain covering manifolds. One of the main results is the following: Let ψ : XPn be a finite covering of the n-dimensional complex projective space branched along a hypersurface with only simple normal crossings and suppose X is nonsingular. Let ci(X) be the i-th Chern class of X. Then (i) if the canonical divisor KX is numerically effective, then (−1)kck(X) (k ≥ 2) is numerically positive, and (ii) if X is of general type, then (−1)ncil (X) cir, (X) > 0, where il + … + ir = n. Furthermore we show that the same properties hold for certain Kummer coverings.  相似文献   

11.
Asymptotic Upper Bounds for Ramsey Functions   总被引:5,自引:0,他引:5  
 We show that for any graph G with N vertices and average degree d, if the average degree of any neighborhood induced subgraph is at most a, then the independence number of G is at least Nf a +1(d), where f a +1(d)=∫0 1(((1−t)1/( a +1))/(a+1+(da−1)t))dt. Based on this result, we prove that for any fixed k and l, there holds r(K k + l ,K n )≤ (l+o(1))n k /(logn) k −1. In particular, r(K k , K n )≤(1+o(1))n k −1/(log n) k −2. Received: May 11, 1998 Final version received: March 24, 1999  相似文献   

12.
Chen’s Conjecture and Its Generalization   总被引:1,自引:0,他引:1  
Let l1, l2, ..., lg be even integers and x be a sufficiently large number. In this paper, the authors prove that the number of positive odd integers k ≤ x such that (k +l1)^2, (k +l2)^2, ..., (k +lg)^2 can not be expressed as 2^n+p^α is at least c(g)x, where p is an odd prime and the constant c(g) depends only on g.  相似文献   

13.
For fixed k ≥ 3, let Ek(x) denote the error term of the sum ?nxrk(n)\sum_{n\le x}\rho_k(n) , where rk(n) = ?n=|m|k+|l|k, g.c.d.(m,l)=1\rho_k(n) = \sum_{n=|m|^k+|l|^k, g.c.d.(m,l)=1} 1. It is proved that if the Riemann hypothesis is true, then E3(x) << x331/1254+eE_3(x)\ll x^{331/1254+\varepsilon} , E4(x) << x37/184+eE_4(x)\ll x^{37/184+\varepsilon} . A short interval result is also obtained.  相似文献   

14.
In this article we prove the following theorem. For any k ≥ 3, let c(k, 1) = exp{exp{kk2}}. If v(v − 1) ≡ 0 (mod k(k −1)) and v − 1 ≡ 0 (mod k−1) and v > c(k, 1), then a B(v,k, 1) exists. © 1996 John Wiley & Sons, Inc.  相似文献   

15.
The spanX n of functionsx i(t)=±1,i=1, …,n, on a setT in the supremum norm is considered. It is proved, for example, thatX n contains an isometric copy ofl 1 k fork≧cM n 2 /n logn whereM n is the Rademacher average of {x i} 1 n . This generalizes a result of Pisier for characters. The proof uses a new combinatorial tool.  相似文献   

16.
Recently, B. Y. Chen introduced a new intrinsic invariant of a manifold, and proved that everyn-dimensional submanifold of real space formsR m (ε) of constant sectional curvature ε satisfies a basic inequality δ(n 1,…,n k )≤c(n 1,…,n k )H 2+b(n 1,…,n k )ε, whereH is the mean curvature of the immersion, andc(n 1,…,n k ) andb(n 1,…,n k ) are constants depending only onn 1,…,n k ,n andk. The immersion is calledideal if it satisfies the equality case of the above inequality identically for somek-tuple (n 1,…,n k ). In this paper, we first prove that every ideal Einstein immersion satisfyingnn 1+…+n k +1 is totally geodesic, and that every ideal conformally flat immersion satisfyingnn 1+…+n k +2 andk≥2 is also totally geodesic. Secondly we completely classify all ideal semi-symmetric hypersurfaces in real space forms. The author was supported by the NSFC and RFDP.  相似文献   

17.
The original Erd s—Rényi theorem states that max0knk+[clogn]i=k+1Xi/[clogn]→α(c),c>0, almost surely for i.i.d. random variables {Xn, n1} with mean zero and finite moment generating function in a neighbourhood of zero. The latter condition is also necessary for the Erd s—Rényi theorem, and the function α(c) uniquely determines the distribution function of X1. We prove that if the normalizing constant [c log n] is replaced by the random variable ∑k+[clogn]i=k+1(X2i+1), then a corresponding result remains true under assuming only the exist first moment, or that the underlying distribution is symmetric.  相似文献   

18.
《Quaestiones Mathematicae》2013,36(3-4):289-302
Abstract

Let d be a positive integer and F be a field of characteristic 0. Suppose that for each positive integer n, I n is a polynomial invariant of the usual action of GLn (F) on Λd(Fn), such that for t ? Λd(F k) and s ? Λd(F l), I k + l (t l s) = I k(t)I t (s), where ts is defined in §1.4. Then we say that {In} is an additive family of invariants of the skewsymmetric tensors of degree d, or, briefly, an additive family of invariants. If not all the In are constant we say that the family is non-trivial. We show that in each even degree d there is a non-trivial additive family of invariants, but that this is not so for any odd d. These results are analogous to those in our paper [3] for symmetric tensors. Our proofs rely on the symbolic method for representing invariants of skewsymmetric tensors. To keep this paper self-contained we expound some of that theory, but for the proofs we refer to the book [2] of Grosshans, Rota and Stein.  相似文献   

19.
Raphael Yuster 《Order》2003,20(2):121-133
Let TT k denote the transitive tournament on k vertices. Let TT(h,k) denote the graph obtained from TT k by replacing each vertex with an independent set of size h≥1. The following result is proved: Let c 2=1/2, c 3=5/6 and c k =1−2k−log k for k≥4. For every ∈>0 there exists N=N(∈,h,k) such that for every undirected graph G with n>N vertices and with δ(G)≥c k n, every orientation of G contains vertex disjoint copies of TT(h,k) that cover all but at most ∈n vertices. In the cases k=2 and k=3 the result is asymptotically tight. For k≥4, c k cannot be improved to less than 1−2−0.5k(1+o(1)). This revised version was published online in June 2006 with corrections to the Cover Date.  相似文献   

20.
For any sequence {ω(n)} n∈ℕ tending to infinity we construct a “quasiquadratic” representation spectrum Λ = {n 2 + o(ω(n))} n∈ℕ: for any almost everywhere (a. e.) finite measurable function f(x) there exists a series in the form $ \mathop \sum \limits_{k \in \Lambda } $ \mathop \sum \limits_{k \in \Lambda } α k ω k (x) that converges a. e. to this function, where {w k (x)} k∈ℕ is the Walsh system. We find representation spectra in the form {n l + o(n l )} n∈ℕ, where l ∈ {2 k } k∈ℕ.  相似文献   

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