Author Keywords: Bounded in probability; convergence in probability; cotype; uniform tightness condition 相似文献
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1.
A random graph Gn(x) is constructed on independent random points U1,…,Un distributed uniformly on [0,1]d, d1, in which two distinct such points are joined by an edge if the l∞-distance between them is at most some prescribed value 0<x<1. The connectivity distance cn, the smallest x for which Gn(x) is connected, is shown to satisfy For d2, the random graph Gn(x) behaves like a d-dimensional version of the random graphs of Erdös and Rényi, despite the fact that its edges are not independent: cn/dn→1, a.s., as n→∞, where dn is the largest nearest-neighbor link, the smallest x for which Gn(x) has no isolated vertices. 相似文献
2.
Y. S. Rama Krishnaiah 《Statistics & probability letters》1990,10(5):439-447
Given \s{Xi, i 1\s} as non-stationary strong mixing (n.s.s.m.) sequence of random variables (r.v.'s) let, for 1 i n and some γ ε [0, 1], and . For any real sequence \s{Ci\s} satisfying certain conditions, let .
F1(x)=γP(Xi<x)+(1-γ)P(Xix)
Ii(x)=γI(Xi<x)+(1-γ)I(Xix)
In this paper an exponential type of bound for P(Dn ), for any >0, and a rate for the almost sure convergence of Dn are obtained under strong mixing. These results generalize those of Singh (1975) for the independent and non-identically distributed sequence of r.v.'s to the case of strong mixing. 相似文献
3.
A mapping ƒ : n=1∞In → I is called a bag mapping having the self-identity if for every (x1,…,xn) ε i=1∞In we have (1) ƒ(x1,…,xn) = ƒ(xi1,…,xin) for any arrangement (i1,…,in) of {1,…,n}; monotonic; (3) ƒ(x1,…,xn, ƒ(x1,…,xn)) = ƒ(x1,…,xn). Let {ωi,n : I = 1,…,n;n = 1,2,…} be a family of non-negative real numbers satisfying Σi=1nωi,n = 1 for every n. Then one calls the mapping ƒ : i=1∞In → I defined as follows an OWA bag mapping: for every (x1,…,xn) ε i=1∞In, ƒ(x1,…,xn) = Σi=1nωi,nyi, where yi is the it largest element in the set {x1,…,xn}. In this paper, we give a sufficient and necessary condition for an OWA bag mapping having the self-identity. 相似文献
4.
J. Arvesú R. Álvarez-Nodarse F. Marcellán K. Pan 《Journal of Computational and Applied Mathematics》1998,90(2):263-156
We obtain an explicit expression for the Sobolev-type orthogonal polynomials {Qn} associated with the inner product , where p(x) = (1 − x)(1 + x)β is the Jacobi weight function, ,β> − 1, A1,B1,A2,B20 and p, q P, the linear space of polynomials with real coefficients. The hypergeometric representation (6F5) and the second-order linear differential equation that such polynomials satisfy are also obtained. The asymptotic behaviour of such polynomials in [−1, 1] is studied. Furthermore, we obtain some estimates for the largest zero of Qn(x). Such a zero is located outside the interval [−1, 1]. We deduce his dependence of the masses. Finally, the WKB analysis for the distribution of zeros is presented. 相似文献
5.
L. Carlitz 《Discrete Mathematics》1980,30(3):211-225
Dumont and Foata have defined a polynomial Fn(x, y, z) recursively. They proved that Fn(x, y, z) is symmetric in x, y, z and that Fn(1, 1, 1) = G2n+2 the Genocchi number. Moreover, they gave an elegant combinatorial interpretation for the coefficients of Fn(x, y, z). In the present paper explicit formulas and generating functions for Fn(x, y, z) are obtained. 相似文献
6.
Victor Reiner 《Discrete Mathematics》1995,140(1-3):129-140
This paper examine all sums of the form where W is a classical Weyl group, X is a one-dimensional character of W, and d(π) is the descent statistic. This completes a picture which is known when W is the symmetric group Sn (the Weyl group An−1). Surprisingly, the answers turn out to be simpler and generalize further for the other classical Weyl groups Bn(Cn) and Dn. The Bn, case uses sign-reversing involutions, while the Dn case follows from a result of independent interest relating statistics for all three groups. 相似文献
7.
Asymptotic behavior of a nonlinear delay difference equation 总被引:1,自引:0,他引:1
J. YanB. Liu 《Applied Mathematics Letters》1995,8(6):1-5
This paper considers a class of nonlinear difference equations . A necessary and sufficient condition for the existence of a bounded nonoscillatory solution is given. 相似文献
Δ3yn + ƒ(n, yn, yn−r) = 0, n N (n0)
8.
Stability of Periodic Orbits and Return Trajectories of Continuous Multi-valued Maps on Intervals 下载免费PDF全文
Let I be a compact interval of real axis R, and(I, H) be the metric space of all nonempty closed subintervals of I with the Hausdorff metric H and f : I → I be a continuous multi-valued map. Assume that Pn =(x_0, x_1,..., xn) is a return tra jectory of f and that p ∈ [min Pn, max Pn] with p ∈ f(p). In this paper, we show that if there exist k(≥ 1) centripetal point pairs of f(relative to p)in {(x_i; x_i+1) : 0 ≤ i ≤ n-1} and n = sk + r(0 ≤ r ≤ k-1), then f has an R-periodic orbit, where R = s + 1 if s is even, and R = s if s is odd and r = 0, and R = s + 2 if s is odd and r 0. Besides,we also study stability of periodic orbits of continuous multi-valued maps from I to I. 相似文献
9.
George Haiman 《Stochastic Processes and their Applications》1999,80(2):231-248
For a 1-dependent stationary sequence {Xn} we first show that if u satisfies p1=p1(u)=P(X1>u)0.025 and n>3 is such that 88np131, thenwhere withandFrom this result we deduce, for a stationary T-dependent process with a.s. continuous path {Ys}, a similar, in terms of P{max0skTYs<u}, k=1,2 formula for P{max0stYsu}, t>3T and apply this formula to the process Ys=W(s+1)−W(s), s0, where {W(s)} is the Wiener process. We then obtain numerical estimations of the above probabilities. 相似文献
P{max(X1,…,Xn)u}=ν·μn+O{p13(88n(1+124np13)+561)}, n>3,
ν=1−p2+2p3−3p4+p12+6p22−6p1p2,μ=(1+p1−p2+p3−p4+2p12+3p22−5p1p2)−1
pk=pk(u)=P{min(X1,…,Xk)>u}, k1
|O(x)||x|.
10.
Let H be a Hopf algebra over a field k and let H A → A, h a → h.a, be an action of H on a commutative local Noetherian kalgebra (A, m). We say that this action is linearizable if there exists a minimal system x1, …, xn of generators of the maximal ideal m such that h.xi ε kx1 + …+ kxn for all h ε H and i = 1, …, n. In the paper we prove that the actions from a certain class are linearizable (see Theorem 4), and we indicate some consequences of this fact. 相似文献
11.
For an integer n3, the crown Sn0 is defined to be the graph with vertex set {x0,x1,…,xn−1,y0,y1,…,yn−1} and edge set {xiyj: 0i,jn−1, i≠j}. In this paper we give some sufficient conditions for the edge decomposition of the crown into isomorphic cycles. 相似文献
12.
Wan-Tong Li 《Applied Mathematics Letters》1997,10(6):101-106
Consider the first-order neutral nonlinear difference equation of the form , where τ > 0, σi ≥ 0 (i = 1, 2,…, m) are integers, {pn} and {qn} are nonnegative sequences. We obtain new criteria for the oscillation of the above equation without the restrictions Σn=0∞ qn = ∞ or Σn=0∞ nqn Σj=n∞ qj = ∞ commonly used in the literature. 相似文献
13.
Yuming Chen 《Applied Mathematics Letters》2002,15(8):1348-979
We propose the difference equation xn+1 = xn − f(xn−k) as a model for a single neuron with no internal decay, where f satisfies the McCulloch-Pitts nonlinearity. It is shown that every solution is truncated periodic with the minimal period 2(2l + 1) for some l ≥ 0 such that (k - l)/(2l + 1) is a nonnegative even integer. The potential application of our results to neural networks is obvious. 相似文献
14.
15.
In this paper we study the existence, the uniqueness, the boundedness and the asymptotic behavior of the positive solutions of the fuzzy difference equation xn+1=∑i=0kAi/xn−ipi, where k{1,2,…,}, Ai, i{0,1,…,k}, are positive fuzzy numbers, pi, i{0,1,…,k}, are positive constants and xi, i{−k,−k+1,…,0}, are positive fuzzy numbers. 相似文献
16.
Renpu Ge 《Applied mathematics and computation》1989,30(3):261-288
This paper gives a parallel computing scheme for minimizing a twice continuously differentiable function with the form where x = (xT1,…,xTm)T and xi Rni, ∑mi = 1ni = n, and n a very big number. It is proved that we may use m parallel processors and an iterative procedure to find a minimizer of ƒ(x). The convergence and convergence rate are given under some conditions. The conditions for finding a global minimizer of ƒ(x by using this scheme are given, too. A similar scheme can also be used parallelly to solve a large scale system of nonlinear equations in the similar way. A more general case is also investigated. 相似文献
17.
Xiang Chen Wang 《Statistics & probability letters》1990,10(5):391-396
Let B be a separable Banach space. The following is one of the results proved in this paper. The Banach space B is of cotype p if and only if
1. dn, n 1, has no subsequence converging in probability, and
2. ∑n 1|an|p < ∞ whenever ∑n 1andn converges almost surely are equivalent for every sequence dn, n 1, of symmetric independent random elements taking values in B.
18.
Maximal IM-unextendable graphs 总被引:3,自引:0,他引:3
A graph G is maximal IM-unextendable if G is not induced matching extendable and, for every two nonadjacent vertices x and y, G+xy is induced matching extendable. We show in this paper that a graph G is maximal IM-unextendable if and only if G is isomorphic to Mr(Ks(Kn1Kn2Knt)), where Mr is an induced matching of size r, r1, t=s+2, and each ni is odd. 相似文献
19.
We have considered the problem of the weak convergence, as tends to zero, of the multiple integral processesin the space
, where fL2([0,T]n) is a given function, and {η(t)}>0 is a family of stochastic processes with absolutely continuous paths that converges weakly to the Brownian motion. In view of the known results when n2 and f(t1,…,tn)=1{t1<t2<<tn}, we cannot expect that these multiple integrals converge to the multiple Itô–Wiener integral of f, because the quadratic variations of the η are null. We have obtained the existence of the limit for any {η}, when f is given by a multimeasure, and under some conditions on {η} when f is a continuous function and when f(t1,…,tn)=f1(t1)fn(tn)1{t1<t2<<tn}, with fiL2([0,T]) for any i=1,…,n. In all these cases the limit process is the multiple Stratonovich integral of the function f. 相似文献
20.
A polynomial in two variables is defined by Cn(x,t)=ΣπΠnx(Gπ,x)t|π|, where Πn is the lattice of partitions of the set {1, 2, …, n}, Gπ is a certain interval graph defined in terms of the partition gp, χ(Gπ, x) is the chromatic polynomial of Gπ and |π| is the number of blocks in π. It is shown that , where S(n, i) is the Stirling number of the second kind and (x)i = x(x − 1) ··· (x − i + 1). As a special case, Cn(−1, −t) = An(t), where An(t) is the nth Eulerian polynomial. Moreover, An(t)=ΣπΠnaπt|π| where aπ is the number of acyclic orientations of Gπ. 相似文献