共查询到20条相似文献,搜索用时 31 毫秒
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.
We consider boundary value problem where 0, λ > 0 are parameters and f C2[0, ∞) such that f(0) < 0. In this paper we study for the cases p (0, β) and p ( β, θ) ( p is the value of the solution at x = 0 and β, θ are such that f( β) = 0, , the relation between λ and the number of interior critical points of the positive solutions of the above system. 相似文献
3.
We prove that the graph of the continuous function has Hausdorff dimension 2, where λ > 1, β > > 1, ( x) = 2 x, 0 x 1/2, (− x) = ( x) and ( x + 1) = ( x). 相似文献
4.
We study the stability of non-negative stationary solutions of where Δ p denotes the p-Laplacian operator defined by Δ pz = div( zp−2z); p > 2, Ω is a bounded domain in RN( N 1) with smooth boundary where [0,1],h:∂Ω→R+ with h = 1 when = 1, λ > 0, and g:Ω×[0,∞)→R is a continuous function. If g( x, u)/ up−1 be strictly increasing (decreasing), we provide a simple proof to establish that every non-trivial non-negative solution is unstable (stable). 相似文献
5.
We consider the existence and stability of an almost periodic solution of the following hybrid system: where if θi≤t<θi+1,i=…−2,−1,0,1,2,…, is an identification function, θi is a strictly ordered sequence of real numbers, unbounded on the left and on the right, pj,j=1,2,…,m, are fixed integers, and the linear homogeneous system associated with (1) satisfies exponential dichotomy. The deviations of the argument are not restricted by any sign assumption when existence is considered. A new technique of investigation of equations with piecewise argument, based on integral representation, is developed. 相似文献
6.
The authors discuss the relation of the oscillation of the following two difference equations, where m ≥ 2, τ : N → N, N isthe set of integers, | n − τ( n)| ≤ Mfor n N0, M is a positive integer, is nondecreasing in x, xf( n, x)> 0, as x ≠ 0. Wewill show some relations of the oscillation of the above two equations. Especially, for m to be even, we establish the equivalenceof the oscillation of the above two difference equations. 相似文献
7.
Eigenvalue interlacing is a versatile technique for deriving results in algebraic combinatorics. In particular, it has been successfully used for proving a number of results about the relation between the (adjacency matrix or Laplacian) spectrum of a graph and some of its properties. For instance, some characterizations of regular partitions, and bounds for some parameters, such as the independence and chromatic numbers, the diameter, the bandwidth, etc., have been obtained. For each parameter of a graph involving the cardinality of some vertex sets, we can define its corresponding weight parameter by giving some “weights” (that is, the entries of the positive eigenvector) to the vertices and replacing cardinalities by square norms. The key point is that such weights “regularize” the graph, and hence allow us to define a kind of regular partition, called “pseudo-regular,” intended for general graphs. Here we show how to use interlacing for proving results about some weight parameters and pseudo-regular partitions of a graph. For instance, generalizing a well-known result of Lovász, it is shown that the weight Shannon capacity Θ* of a connected graph Γ, with n vertices and (adjacency matrix) eigenvalues λ1 > λ2 … λn, satisfies where Θ is the (standard) Shannon capacity and v is the positive eigenvector normalized to have smallest entry 1. In the special case of regular graphs, the results obtained have some interesting corollaries, such as an upper bound for some of the multiplicities of the eigenvalues of a distance-regular graph. Finally, some results involving the Laplacian spectrum are derived. 相似文献
8.
In this paper, we prove a Chebyshev type inequality for fuzzy integrals. More precisely, we show that: where μ is the Lebesgue measure on and f,g:[0,1]→[0,∞) are two continuous and strictly monotone functions, both increasing or both decreasing. Also, some examples and applications are presented. 相似文献
9.
We use Adomian decomposition method for solving the fractional nonlinear two-point boundary value problem where D is Caputo fractional derivative, c is a constant, μ > 0, and F:[0,1]×[0,∞)→[0,∞) a continuous function. The fractional Bratu problem is solved as an illustrative example. 相似文献
10.
The weighted Newton–Cotes quadrature rules of open type are denoted by where w( x) is a positive function and is the step size. Various cases can be selected for the weight function of the above formula. In this paper, we consider as the main weight function and study the general formula: The precision degree of the above formula is n + 1 for even n’s and is n for odd n’s but if one considers its upper and lower bounds as two additional variables, a nonlinear system will be derived whose solution improves the precision degree of above formula up to degree n + 2 numerically. In this way, some examples are given to show the numerical superiority of our idea. 相似文献
11.
This article is contributed to the Cauchy problem u/t = △u K(ㄧxㄧ)up in Rn x (0,T), u(x,0) =(ψ)(x) in Rn; with initial function(ψ)≠0. The stability of positive radial steady state, which are positive solutions of △u K(ㄧxㄧ)up =0, is obtained when p is critical for general K(ㄧxㄧ). 相似文献
12.
An asymptotic expansion is constructed for the solution of the initial-value problem when t is restricted to the interval [0,T/ε], where T is any given number. Our analysis is mathematically rigorous; that is, we show that the difference between the true solution u(t,x;ε) and the Nth partial sum of the asymptotic series is bounded by εN+1 multiplied by a constant depending on T but not on x and t. 相似文献
13.
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
14.
This paper presents the finding that the invocation of new words in human language samples is governed by a slowly changing Poisson process. The time dependent rate constant for this process has the form λ(t) = λ1(1−λ2t)e-λ2t+λ3(1−λ4t)e-λ4t+λ5 , where . This form implies that there are opening, middle and final phases to the introduction of new words, each distinguished by a dominant rate constant, or equivalently, rate of decay. With the occasional exception of the phase transition from beginning to middle, the rate λ(t) decays monotonically. Thus, λ(t) quantifies how the penchant of humans to introduce new words declines with the progression of their narratives, written or spoken. 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.
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
17.
The combinatorial tool of generating functions for restricted partitions is used to generalize a quantum physics theorem relating distinct multiplets of different angular momenta in the composite Fermion model of the fractional quantum Hall effect. Specifically, if gℓ(N,M) denotes the number of distinct multiplets of angular momentum ℓ and total angular momentum M, we prove that where the sum is taken over all positive divisors of N and L(k)=kℓ-kN/2+3k/2-N+N/(2k)-1/2. The original Quinn–Wójs theorem results when k=1 and it appears that this generalization will be useful in further investigations of nuclear shells modeling elementary particle interactions when the particles are clustered together. 相似文献
18.
In this work, the authors first show the existence of global attractors for the following lattice complex Ginzburg–Landau equation: and for the following lattice Schrödinger equation: Then they prove that the solutions of the lattice complex Ginzburg–Landau equation converge to that of the lattice Schrödinger equation as ε→0+. Also they prove the upper semicontinuity of as ε→0+ in the sense that . 相似文献
19.
In this paper, we study the singular perturbation problem where 0<ε1 is a small positive parameter, p(x) and q(x) are sufficiently smooth and strictly positive functions. The main feature of this equation is that there are two second-order turning points in the interval (0,1). Based on the rigorous results on singular perturbation problems with one second-order turning point in our previous work, we obtain a uniform asymptotic approximation for the general solution of the above equation by means of a matching technique. 相似文献
20.
We investigate two families of Lorenz-like three-dimensional nonlinear dynamical systems (i) the generalized Lorenz system and (ii) the Burke–Shaw system. Analytical investigation of the former system is possible under the assumption (I) which in fact concerns four different systems corresponding to = ±1, m = 0, 1. The fixed points and stability characteristics of the Lorenz system under the assumption (I) are also classified. Parametric and temporal ( t → ∞) asymptotes are also studied in connection to the memory of both the systems. We calculate the Lyapunov exponents and Lyapunov dimension for the chaotic attractors in order to study the influence of the parameters of the Lorenz system on the attractors obtained not only when the assumption (I) is satisfied but also for other values of the parameters σ, r, b, ω and m. 相似文献
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