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1.
具有最大亏量和的亚纯函数   总被引:1,自引:0,他引:1  
Theorem 1 Let F(z) be a finite order meromorphic function satisfying Theorem 2 Let F(z) satisfy the condition of Theorem 1 and δ(0,F) < 1. Then δ(0, F′/F) = 0.  相似文献   

2.
Let F be a field with characteristic 0,V=F~n the n-dimensional vector space over F and let G be a finite pseudo-reflection group which acts on V.Let χ:G→F~* be a 1-dimensional representation of G.In this article we show that X(g)=(detg)~α(0≤α≤r-1),where g∈G and r is the order of g.In addition,we characterize the relation between the relative invariants and the invariants of the group G,and then we use Molien's Theorem of invariants to compute the Poincaré series of relative invariants.  相似文献   

3.
In this paper we have proved Theorem 2. Let T be an operator on the Hilbert space II with the single valued extension property, Suppose that for every X in the complex plane, it holds that $||(T-\lambda)f||^2 \leq ||(T-\lambda)^2f||\cdot ||f||,\forall f \in H$ Then for any closed subset \delta of the plane, the spectral subspace £_T (\delta) is closed. Theorem 9. Let T and S^* be semi-hyponormal operators and 0 \notin \sigma_p(s). Suppose that there exists an injective operator W with dense range which satisfies TW = WS. Then T and S are normal operators. Theorem 10. Let S be a co-semi-hyponormal operator with the single valued extension property and be not normal. Then there exists f \ne 0 which satisfies ${\sigma _s}(f) \not\subset \sigma (S)$  相似文献   

4.
In this paper,we shall mainly study the p-solvable finite group in terms of p-local rank,and a group theoretic characterization will be given of finite p-solvabel groups with p-local rank two.Theorem A Let G be a finite p-solvable group with p-local rank plr(G)=2 and Op(G)=1.If P is a Sylow p-subgrounp of G,then P has a normal subgroup Q such that P/Q is cyclic or a generalized quaternion 2-group and the p-rank of Q is at most two.Theorem B Let G be a finite p-solvable group with Op(G)=1.Then the p-length lp(G)≤plr(G);if in addition plr(G)=lp (G) and p≥5 is odd,then plr(G)=0 or 1.  相似文献   

5.
Let F be a field with characteristic 0, V = Fn the n-dimensional vector space over F and let G be a finite pseudo-reflection group which acts on V . Let χ : G→ F* be a 1- dimensional representation of G. In this article we show that χ(g) = (detg)α(0 ≤ α ≤ r - 1), where g ∈ G and r is the order of g. In addition, we characterize the relation between the relative invariants and the invariants of the group G, and then we use Molien’s Theorem of invariants to compute the Poincar′e series of relative invariants.  相似文献   

6.
Let p ≥ 2 be a prime number and Z_(p) be the ring of p-adic intergers. Let G be a semigroup generated by infinitely many contractive maps on p Z_(p). It is shown that if G satisfies the open tiling conditions, then there exists a shift transformation on the limit set of G and the shift transformation is ergodic with respect to the Haar measure on p Z_(p). As an application, we can generalize p-adic Khinchin's Theorem and p-adic Lochs' Theorem to any infinitely generated semigroup by use of the ergodicity of the shift transformation.  相似文献   

7.
一类牛顿插值级数的推广   总被引:2,自引:1,他引:1  
Theorem 1 Let ψ(r) be a really continuous and differentiable function on [0,∞) to satisfy that.  相似文献   

8.
1 Introduction and Main ResultsLet {X.,n > 1} be a sequence of random variables in the same probability space andnput Sn = Z Xj, n 2 1. ln real-valued case1 the rates of convergence to zero of qualltitiesi = 1P(lS.I/n'/' > E) (0 < f < 2) are described by the well-known theorem of Baum and Katz(1965):Theorem BK Let 0 < t < 2,r 2 1, and let {X., n 2 1} be real valued iid r.v.'s, when1 5 t < 2, EXl = 0. ThenIn l985, Bai and Su generalized Theorem BK and obtained the correspondillg resul…  相似文献   

9.
Let G be an abelian p-group and K be a field of the first kind with respect to p of char K ≠p and of sp(K) = N or NU {0}. Then it is shown that the normed Sylow p-subgroup S(KG) is torsion complete if and only if G is bounded (Theorem 1). An analogous fact is proved for the case when K is of the second kind (Theorem 2). These completely settle a conjecture posed by us in Compt. Rend. Acad. Bulg. Sci. (1993) and are also a supplement to our result in the modular case published in Acta Math. Hungar. (1997).  相似文献   

10.
Let T denote a tree with the diameter d(d≥2) and order n. Let P^*d,r,n-d-1denote the tree obtained by identifying the rth vertex of path Pd l and the center of starKl,K1,n-d-1, where r = r(d) is the integer part about d 2/2. Then p(T)≤ p(P^*d,r,n-d-1), andequality holds if and only if T≌P^*d,r,n-d-1  相似文献   

11.
Let Ωbelong to R^m (m≥ 2) be a bounded domain with piecewise smooth and Lipschitz boundary δΩ Let t and r be two nonnegative integers with t ≥ r + 1. In this paper, we consider the variable-coefficient eigenvalue problems with uniformly elliptic differential operators on the left-hand side and (-Δ)^T on the right-hand side. Some upper bounds of the arbitrary eigenvalue are obtained, and several known results are generalized.  相似文献   

12.
Let be a bipartite distance-regular graph of even valencyk. Let us consider the intersection array modulo 2, which would become Lett be the length of any series of (1, 0, 1)'s witht > 1. Thent + 1|r 1 + 1, withr 1 the length of the first series.  相似文献   

13.
Let G be a group, t an unknown, and r(t) an element of the free product G* ? t?. The equation r(t) = 1 has a solution over G if it has a solution in a group H containing G. The Kervaire–Laudenbach (KL) conjecture asserts that if the exponent sum of t in r(t) is nonzero the equation has a solution. Equations of length 5 have been studied and it was proved that a solution exists under certain restrictions imposed on the coefficients of the equation. This article removes these restrictions and therefore settles the KL conjecture for equations of length five.  相似文献   

14.
Let G be a finite abelian group with exp(G) = e. Let s(G) be the minimal integer t with the property that any sequence of t elements in G contains an e-term subsequence with sum zero. Let n, mand r be positive integers and m ≥ 3. Furthermore, η(C m r ) = a r (m − 1) + 1, for some constant a r depending on r and n is a fixed positive integer such that
$ n \geqslant \frac{{m^r (c(r)m - a_r (m - 1) + m - 3)(m - 1) - (m + 1) + (m + 1)(a_r + 1)}} {{m(m + 1)(a_r + 1)}} $ n \geqslant \frac{{m^r (c(r)m - a_r (m - 1) + m - 3)(m - 1) - (m + 1) + (m + 1)(a_r + 1)}} {{m(m + 1)(a_r + 1)}}   相似文献   

15.
Let t(n) denote the greatest number of arcs in a diagraph of orders n which does not contain any antidrected cycles. We show that [16/5(n ? 1)] ≤ t(n) ≤ 1/2 (n ? 1) for n ≥ 5. Let tr (n) denote the corresponding quantity for r-colorable digraphs. We show that [16/5(n ? 1)] ≤ t5(n) ≤ t6(n) ≤ 10/3(n ? 1) for n ≥ 5 and that t4(n) = 3(n ? 1) for n ≥ 3.  相似文献   

16.
Dedicated to the memory of Paul Erdős Let f(r,p,t) (p > t >= 1, r >= 2) be the maximum of the cardinality of a minimum transversal over all r-uniform hypergraphs possessing the property that every subhypergraph of with p edges has a transversal of size t. The values of f(r,p,2) for p = 3, 4, 5, 6 were found in [1] and bounds on f(r,7,2) are given in [3]. Here we prove that for large p and huge r. Received September 23, 1999 RID="*" ID="*" This work was partially supported by the grant 99-01-00581 of the Russian Foundation for Fundamental Research and the Dutch–Russian Grant NWO-047-008-006.  相似文献   

17.
Chen, Lih, and Wu conjectured that for r ≥ 3, the only connected graphs with maximum degree at most r that are not equitably r-colorable are K r,r (for odd r) and K r+1. If true, this would be a strengthening of the Hajnal-Szemerédi Theorem and Brooks’ Theorem. We extend their conjecture to disconnected graphs. For r ≥ 6 the conjecture says the following: If an r-colorable graph G with maximum degree r is not equitably r-colorable then r is odd, G contains K r,r and V(G) partitions into subsets V 0, …, V t such that G[V 0] = K r,r and for each 1 ≤ it, G[V i ] = K r . We characterize graphs satisfying the conclusion of our conjecture for all r and use the characterization to prove that the two conjectures are equivalent. This new conjecture may help to prove the Chen-Lih-Wu Conjecture by induction.  相似文献   

18.
An optimal solution for the following “chess tournament” problem is given. Let n, r be positive integers such that r<n. Put N=2n, R=2r+1. Let XN,R be the set of all ordered pairs (T, A) of matrices of degree N such that T=(tij) is symmetric, A=(aij) is skew-symmetric, tij ∈,{0, 1, 2,…, R), aij ∈{0,1,–1}. Moreover, suppose tii=aii=0 (1?i?N). tij = tik>0 implies j=k, tij=0 is equivalent to aij=0, and |ai1|+|ai2|+…+|aiN|=R (1?i?N). Let p(T, A) be the number of i such that 1?i?N and ai1 + ai2 + … + aiN >0. The main result of this note is to show that max p(T, A) for (T, A)∈XN, R is equal to [n(2r+1)/(r+1)], and a pair (T0, A0) satisfying p(T0, A0)=[n(2r+1)/(r+1)] is also given.  相似文献   

19.
Let p be a prime number, let K be a field of characteristic not p, containing the p-th roots of unity, and let r≥1 be an integer. We compute the essential dimension of ℤ/p r ℤ over K (Theorem 4.1). In particular, i) We have ed(ℤ/8ℤ)=4, a result which was conjectured by Buhler and Reichstein in 1995 (unpublished). ii) We have ed(ℤ/p r ℤ)≥p r-1.  相似文献   

20.
Let (zj) be a sequence of complex numbers satisfying |zj| ∞ asj → ∞ and denote by n(r) the number of zj satisfying |zj|≤ r. Suppose that lim infr → ⇈ log n(r)/ logr > 0. Let ϕ be a positive, non-decreasing function satisfying ∫ (ϕ(t)t logt)−1 dt < ∞. It is proved that there exists an entire functionf whose zeros are the zj such that log log M(r,f) = o((log n(r))2ϕ(log n(r))) asr → ∞ outside some exceptional set of finite logarithmic measure, and that the integral condition on ϕ is best possible here. These results answer a question by A. A. Gol’dberg.  相似文献   

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