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1.
We present a characterization of those Euclidean distance matrices (EDMs) D which can be expressed as D=λ( E− C) for some nonnegative scalar λ and some correlation matrix C, where E is the matrix of all ones. This shows that the cones where
is the elliptope (set of correlation matrices) and
is the (closed convex) cone of EDMs. The characterization is given using the Gale transform of the points generating D. We also show that given points
, for any scalars λ1,λ2,…,λn such that we have ∑j=1nλjpi−pj2= forall i=1,…,n, for some scalar independent of i. 相似文献
2.
This paper considers a class of nonlinear difference equations Δ3yn + ƒ(n, yn, yn−r) = 0, n N (n0) . A necessary and sufficient condition for the existence of a bounded nonoscillatory solution is given. 相似文献
3.
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], F1(x)=γP(Xi<x)+(1-γ)P(Xix) and Ii(x)=γI(Xi<x)+(1-γ)I(Xix) . For any real sequence \s{ Ci\s} satisfying certain conditions, let . 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
4.
Oscillation criteria for the second-order half-linear differential equation [r(t)|ξ′(t)|−1 ξ′(t)]′ + p(t)|ξ(t)|−1ξ(t)=0, t t0 are established, where > 0 is a constant and
exists for t [ t0, ∞). We apply these results to the following equation: where
, D = ( D1,…, DN), Ω a = x
N : |x| ≥ a} is an exterior domain, and c C([a, ∞),
), n > 1 and N ≥ 2 are integers. Here, a > 0 is a given constant. 相似文献
5.
Using the integral average method, we establish some oscillation criteria of Kamenev type and Yan type for the nonlinear system of differential equation where the functions bi( t) ( i = 1, 2) are nonnegative and summable on each finite segment of the interval Z0, ∞), λ i > 0 ( i = 1,2) with λ 1 λ 2 = 1. 相似文献
6.
We establish an explicit formula for the number of Latin squares of order n: , where Bn is the set of n× n(0,1) matrices, σ 0( A is the number of zero elements of the matrix A and per A is the permanent of the matrix A. 相似文献
7.
In 1994, van Trung (Discrete Math. 128 (1994) 337–348) [9] proved that if, for some positive integers d and h, there exists an Sλ( t, k, v) such that then there exists an Sλ(v−t+1)( t, k, v+1) having v+1 pairwise disjoint subdesigns Sλ( t, k, v). Moreover, if Bi and Bj are any two blocks belonging to two distinct such subdesigns, then d| Bi∩ Bj|< k− h. In 1999, Baudelet and Sebille (J. Combin. Des. 7 (1999) 107–112) proved that if, for some positive integers, there exists an Sλ( t, k, v) such that where m=min{ s, v− k} and n=min{ i, t}, then there exists an having
pairwise disjoint subdesigns Sλ( t, k, v). The purpose of this paper is to generalize these two constructions in order to produce a new recursive construction of t-designs and a new extension theorem of t-designs. 相似文献
8.
Let X1, X2, … be independent identically distributed random variables. Then, Hsu and Robbins (1947) together with Erdös (1949, 1950) have proved that , if and only if E[X21] < ∞ and E[X1] = 0. We prove that there are absolute constants C1, C2 (0, ∞) such that if X1, X2, … are independent identically distributed mean zero random variables, then c1λ−2 E[X12·1{|X1|λ}]S(λ)C2λ−2 E[X12·1{|X1|λ}] , for every λ > 0. 相似文献
9.
We shall establish some new criteria for the oscillation of all solutions of higher-order difference equations of the form δm(xn-xn-r)+qnf(xn-g=0, m1 相似文献
10.
For the pth-order linear ARCH model, , where 0 > 0, i 0, I = 1, 2, …, p, { t} is an i.i.d. normal white noise with Et = 0, Et2 = 1, and t is independent of { Xs, s < t}, Engle (1982) obtained the necessary and sufficient condition for the second-order stationarity, that is, 1 + 2 + ··· + p < 1. In this note, we assume that t has the probability density function p( t) which is positive and lower-semicontinuous over the real line, but not necessarily Gaussian, then the geometric ergodicity of the ARCH( p) process is proved under Et2 = 1. When t has only the first-order absolute moment, a sufficient condition for the geometric ergodicity is also given. 相似文献
11.
Let {ζ k} be the normalized sums corresponding to a sequence of i.i.d. variables with zero mean and unit variance. Define random measures and let G be the normal distribution. We show that for each continuous function h satisfying ∫ hd G<∞ and a mild regularity assumption, one has a.s. 相似文献
12.
In the present paper, we consider the following generalization of Besicovitch functions. Let {λ n} satisfy Hadamard condition, write We are interested in the intrinsic relationship among the coefficients {an}, the modulus of continuity of f and the upper Box dimension of graph of f. Especially, constructive structure of the function f which can be deduced from the (upper) Box dimension is a very interesting subject, and is hardly ever touched upon as far as we are aware. 相似文献
13.
We prove that for λ ≥ 0, p ≥ 3, there exists an open ball B L2(0,1) such that the problem − (|u′|p−2 u′)′ − λ|u|p−2u = f, in (0,1) , subject to certain separated boundary conditions on (0,1), has a solution for f B. 相似文献
14.
In the present note we study the threshold first-order bilinear model X(t)=aX(t−1)+(b11{X(t−1)<c}+b21{X(t−1)c})X(t−1)e(t−1)+e(t), tεN where { e( t), tε N} is a sequence of i.i.d. absolutely continuous random variables, X(0) is a given random variable and a, b1, b2 and c are real numbers. Under suitable conditions on the coefficients and lower semicontinuity of the densities of the noise sequence, we provide sufficient conditions for the existence of a stationary solution process to the present model and of its finite moments of order p. 相似文献
15.
Consider the first-order neutral nonlinear difference equation of the form , where τ > 0, σ i ≥ 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 Σ n=0∞ qn = ∞ or Σ n=0∞ nqn Σ j=n∞ qj = ∞ commonly used in the literature. 相似文献
16.
In this paper, we shall show that under suitable conditions on f and K, the inequalities imply that the integro-differential inequalities have no positive solutions, respectively. 相似文献
17.
Let { A( t)}−∞< t<∞ be Lévy's stochastic area process and assume { W( t)} t0 is an independent Brownian motion. Then we prove the following local law of the iterated logarithm for the composed process { A( W( t))} t;0: . 相似文献
18.
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 88 np131, then P{max(X1,…,Xn)u}=ν·μn+O{p13(88n(1+124np13)+561)}, n>3, where ν=1−p2+2p3−3p4+p12+6p22−6p1p2,μ=(1+p1−p2+p3−p4+2p12+3p22−5p1p2)−1 with pk=pk(u)=P{min(X1,…,Xk)>u}, k1 and From this result we deduce, for a stationary T-dependent process with a.s. continuous path { Ys}, a similar, in terms of P{max 0skTYs< u}, k=1,2 formula for P{max 0stYsu}, t>3 T 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
19.
Consider two transient Markov processes ( Xvt) tεR·, ( Xμt) tεR· with the same transition semigroup and initial distributions v and μ. The probability spaces supporting the processes each are also assumed to support an exponentially distributed random variable independent of the process. We show that there exist (randomized) stopping times S for (Xvt), T for (Xμt) with common final distribution, L(XvS|S < ∞) = L(XμT|T < ∞), and the property that for t < S, resp. t < T, the processes move in disjoint portions of the state space. For such a coupling (S, T) it is shown where
denotes the bounded harmonic functions of the Markov transition semigroup. Extensions, consequences and applications of this result are discussed. 相似文献
20.
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
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