共查询到20条相似文献,搜索用时 171 毫秒
1.
《数学的实践与认识》2015,(11)
设P[A,B]为著名的Janowski函数类.定义函数族的三阶哈达玛乘积为Q_1*Q_2*Q_3={f_1*f_2*f_3(z):f_1∈Q_1,f_2∈Q_2,f_3∈Q_3}.讨论并得到了P(A_1,B_1)*P(A_2,B_2)*P(A_3,B_3)=P(X,Y)的充要条件. 相似文献
2.
设 f 是由以下不可约方程所定义的 n 值代数体函数:ψ(z,f)≡A_0(z)f~n+A_1(z)f~(n-1)+…+A_(n-1)(z)f+A_n(z)=0,(1)这里,A_0(z),A_1(z),…,A_n(z)是没有公共零点的整函数,设 f_1,f_2,…,f_n 是 f 的 n 个分支,称 相似文献
3.
Wei Gengping~ Shen Jianhua~ 《高校应用数学学报(英文版)》2006,21(3):320-326
This paper studies the nonautonomous nonlinear system of difference equationsΔx(n)=A(n)x(n)+f(n,x(n)),n∈Z,(*) where x(n)∈R~N,A(n)=(a_(ij)(n))N×N is an N×N matrix,with a-(ij)∈C(R,R) for i,j= 1,2,3,...,N,and f=(f_1,f_2,...,f_N)~T∈C(R×R~N,R~N),satisfying A(t+ω)=A(t),f(t+ω,z)=f(t,z) for any t∈R,(t,z)∈R×R~N andωis a positive integer.Sufficient conditions for the existence ofω-periodic solutions to equations (*) are obtained. 相似文献
4.
Let A, B be two sets and f:A→B a map. The iterates f~n: A_n→B,n=1,2,…aredefined inductively by A_1=A, f~1=f and A_1=f~(-1)(A_(n-1)∩B), f~n=f~(n-1)(f) for n≥2.Note that A_2=f~(-1)(A_1∩B)A=A_1 and thus A_n A_(n-1) A for n≥2. A point x∈A is called a periodic point of period n of f if x∈A_n and f~n(x)=x, butf_j(x)≠x for any j less than n. A periodic point of period 1 is called a fixpoint. Then a periodic 相似文献
5.
研究了高阶线性微分方程f~(k)+A_(k-1)(z)f~(k-1)+…+A_1(z)f′+A_0(z)f=0的非零解f,及其一阶、二阶导数,f~(i)(i=1,2)的不动点性质,这里A_j(z)(j=0,1,…k-1)为亚纯函数,得到了若δ(∞,A_0)>0,且满足max{i(A1),i(A2),…,i(A_(k-1))}相似文献
6.
杨国孝 《纯粹数学与应用数学》1991,7(2):110-112
命A表示单位园盘△={z:|z|<1}内解析的函数的集合,A_0={f(z):f(z)∈A,f(0)=0}。 B_0={w(z):w(z)∈A_0,|w(z)|<1,z∈△}对任意固定的实常数a,b,-1≤b相似文献
7.
For a tuple A=(A_1,A_2,…,A_n) of elements in a unital algebra B over C,its projective spectrum P(A) or p(A) is the collection of z∈C~n,or respectively z∈P~(n-1),such that A(z)=z_1A_1+z_2A_2+…+z_nA_n is not invertible in Β.The first half of this paper proves that if B is Banach then the resolvent set P~c(A) consists of domains of holomorphy.The second half computes the projective spectrum for the generating vectors of a Clifford algebra.The Chern character of an associated kernel bundle is shown to be nontrivial. 相似文献
8.
《数学研究与评论》1991,(4)
Let H(D)be the collection of functions which are analytic in the unitdisc D.we call B_0={f∈H(D),(?)(1-|z|~2)|f’(z)|=0}litlle Bloch space.Letf∈H(D),0
相似文献
9.
选择题 (每小题 5分 ,12小题共 6 0分 .在每小题给出的四个选项中 ,只有一项是符合题目要求的 )1.集合M ={x|x =2n ,n∈Z} ,N ={x|x =2n +1,n∈Z} ,P ={x|x =4n +1,n∈Z} ,x∈M ,y∈N ,则必有 ( )(A)x +y∈M .(B)x +y∈N .(C)x +y∈P .(D)x +y M ,N ,P任何一个 .2 .已知集合M =- 1,0 ,1,f是从M到M的映射 ,则满足 f(- 1) +f(0 ) +f(1) =0的映射有( )(A) 6个 . (B) 7个 . (C) 8个 . (D) 9个 .3.已知f0 (x ) =f (x ) =x +1(x≤ 1) ,-x +3(x >1) ,fn +1(x) =f [fn (x ) ],则f2 (- 12 ) = ( )(A) - 12 . (B) 32 … 相似文献
10.
《数学研究与评论》1984,(4)
1 Introduction We denote that: σ—the class of functions ω(z)=A_1z+A_2z~2+…regular in the unit disk such that sum from n=1 to ∞ (n|A_n|~2<∞);K_c— the class of close-to-convex function f(z),that is, if f(z)=α_1z+α_2z~2+…there exists a starlike function g(z) =b_1z+b_2z~2+…such that 相似文献
11.
Harris Kwong 《Discrete Mathematics》2008,308(23):5522-5532
Let G be a graph with vertex set V and edge set E, and let A be an abelian group. A labeling f:V→A induces an edge labeling f∗:E→A defined by f∗(xy)=f(x)+f(y). For i∈A, let vf(i)=card{v∈V:f(v)=i} and ef(i)=card{e∈E:f∗(e)=i}. A labeling f is said to be A-friendly if |vf(i)−vf(j)|≤1 for all (i,j)∈A×A, and A-cordial if we also have |ef(i)−ef(j)|≤1 for all (i,j)∈A×A. When A=Z2, the friendly index set of the graph G is defined as {|ef(1)−ef(0)|:the vertex labelingf is Z2-friendly}. In this paper we completely determine the friendly index sets of 2-regular graphs. In particular, we show that a 2-regular graph of order n is cordial if and only if n?2 (mod 4). 相似文献
12.
Let [n] denote the set of positive integers {1,2,…,n}. An r-partial permutation of [n] is a pair (A,f) where A⊆[n], |A|=r and f:A→[n] is an injective map. A set A of r-partial permutations is intersecting if for any (A,f), (B,g)∈A, there exists x∈A∩B such that f(x)=g(x). We prove that for any intersecting family A of r-partial permutations, we have .It seems rather hard to characterize the case of equality. For 8?r?n-3, we show that equality holds if and only if there exist x0 and ε0 such that A consists of all (A,f) for which x0∈A and f(x0)=ε0. 相似文献
13.
YangChangsen 《高校应用数学学报(英文版)》2001,16(3):285-289
Abstract. Suppose H is a complex Hilbert space, AH (△) denotes the set of all analytic operator functions on 相似文献
14.
Hiro Ito 《Discrete Applied Mathematics》2006,154(16):2330-2334
Let H=(N,E,w) be a hypergraph with a node set N={0,1,…,n-1}, a hyperedge set E⊆2N, and real edge-weights w(e) for e∈E. Given a convex n-gon P in the plane with vertices x0,x1,…,xn-1 which are arranged in this order clockwisely, let each node i∈N correspond to the vertex xi and define the area AP(H) of H on P by the sum of the weighted areas of convex hulls for all hyperedges in H. For 0?i<j<k?n-1, a convex three-cut C(i,j,k) of N is {{i,…,j-1}, {j,…,k-1}, {k,…,n-1,0,…,i-1}} and its size cH(i,j,k) in H is defined as the sum of weights of edges e∈E such that e contains at least one node from each of {i,…,j-1}, {j,…,k-1} and {k,…,n-1,0,…,i-1}. We show that the following two conditions are equivalent:
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- AP(H)?AP(H′) for all convex n-gons P.
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- cH(i,j,k)?cH′(i,j,k) for all convex three-cuts C(i,j,k).
15.
16.
László Lovász 《Journal of Combinatorial Theory, Series A》2006,113(4):726-735
We prove the following theorem, which is an analog for discrete set functions of a geometric result of Lovász and Simonovits. Given two real-valued set functions f1,f2 defined on the subsets of a finite set S, satisfying for i∈{1,2}, there exists a positive multiplicative set function μ over S and two subsets A,B⊆S such that for i∈{1,2}μ(A)fi(A)+μ(B)fi(B)+μ(A∪B)fi(A∪B)+μ(A∩B)fi(A∩B)?0. The Ahlswede-Daykin four function theorem can be deduced easily from this. 相似文献
17.
Eliyahu Beller 《Israel Journal of Mathematics》1975,22(1):68-80
The functionf(z), analytic in the unit disc, is inA p if \(\int {\int {_{\left| z \right|< 1} \left| {f(z)} \right|^p dxdy< \infty } } \) . A necessary condition on the moduli of the zeros ofA p functions is shown to be best possible. The functionf(z) belongs toB p if \(\int {\int {_{\left| z \right|< 1} \log ^ + \left| {f(z)} \right|)^p } } \) . Let {z n } be the zero set of aB p function. A necessary condition on |z n | is obtained, which, in particular, implies that Σ(1?|z n |)1+(1/p)+g <∞ for all ε>0 (p≧1). A condition on the Taylor coefficients off is obtained, which is sufficient for inclusion off inB p. This in turn shows that the necessary condition on |z n | is essentially the best possible. Another consequence is that, forq≧1,p<q, there exists aB p zero set which is not aB q zero set. 相似文献
18.
Gustav Nordh 《Discrete Mathematics》2008,308(9):1653-1664
A Skolem sequence is a sequence s1,s2,…,s2n (where si∈A={1,…,n}), each si occurs exactly twice in the sequence and the two occurrences are exactly si positions apart. A set A that can be used to construct Skolem sequences is called a Skolem set. The problem of deciding which sets of the form A={1,…,n} are Skolem sets was solved by Thoralf Skolem in the late 1950s. We study the natural generalization where A is allowed to be any set of n positive integers. We give necessary conditions for the existence of Skolem sets of this generalized form. We conjecture these necessary conditions to be sufficient, and give computational evidence in favor of our conjecture. We investigate special cases of the conjecture and prove that the conjecture holds for some of them. We also study enumerative questions and show that this problem has strong connections with problems related to permutation displacements. 相似文献
19.
Manfred Stoll 《Potential Analysis》1995,4(2):141-155
In the paper we investigate tangential boundary limits of invariant Green potentials on the unit ballB in ? n ,n≥1. LetG(z, w) denote the Green function for the Laplace-Beltrami operator onB, and let λ denote the invariant measure onB. If μ is a non-negative measure, orf is a non-negative measurable function onB,G μ andG f denote the Green potential of μ andf respectively. For ξ∈S=δB, τ≥1, andc>0, let $$\mathcal{T}_{\tau ,c} (\zeta ) = \{ z \in B:\left| {1 - \left\langle {z,\xi } \right\rangle } \right|^\tau< c(1 - \left| z \right|^2 )\} $$ . The main result of the paper is as follows: Letf be a non-negative measurable function onB satisfying $$\int_B {(1 - \left| w \right|^2 )^\beta f^p (w)d\lambda (w)< \infty } $$ for some β, 0<β<n, and somep>n. Then for each τ, 1≤τ<n/β, there exists a setE t ?S withH βτ (E t )=0, such that $$\mathop {\lim }\limits_{\mathop {z \to \zeta }\limits_{z \in \mathcal{T}_{\tau ,c} (\zeta )} } G_f (z) = 0,forall\zeta \in S \sim E_\tau $$ In the above, for 0<α≤n,H α denotes the non-isotropic α-dimensional Hausdorff capacity onS. We also prove that if {a k } is a sequence inB satisfying Σ(1?|a k |2) β <∞ for some β, 0 <β<n, and μ=Σδ ak , where δ a denotes point mass measure ata, then the same conclusion holds for the potentialG μ . 相似文献
20.
Motivated by the discovery that the eighth root of the theta series of the E8 lattice and the 24th root of the theta series of the Leech lattice both have integer coefficients, we investigate the question of when an arbitrary element f∈R (where R=1+xZ?x?) can be written as f=gn for g∈R, n?2. Let Pn:={gn|g∈R} and let . We show among other things that (i) for f∈R, f∈Pn⇔f (mod μn)∈Pn, and (ii) if f∈Pn, there is a unique g∈Pn with coefficients mod μn/n such that f≡gn (mod μn). In particular, if f≡1 (mod μn) then f∈Pn. The latter assertion implies that the theta series of any extremal even unimodular lattice in Rn (e.g. E8 in R8) is in Pn if n is of the form i2j3k5 (i?3). There do not seem to be any exact analogues for codes, although we show that the weight enumerator of the rth order Reed-Muller code of length m2 is in Pr2 (and similarly that the theta series of the Barnes-Wall lattice BWm2 is in Pm2). We give a number of other results and conjectures, and establish a conjecture of Paul D. Hanna that there is a unique element f∈Pn (n?2) with coefficients restricted to the set {1,2,…,n}. 相似文献