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1.
Let q( x) be a real-valued function with compact support D⊂ℝ 3. Given the scattering amplitude A(α′, α, k) for all α′, α∈ S2 and a fixed frequency k>0, the moments of q( x) up to the second order are found using a computationally simple and relatively stable two-step procedure. First, one finds the zeroth moment (total intensity) and the first moment (centre of inertia) of the potential q. Second, one refines the above moments and finds the tensor of the second central moments of q. Asymptotic error estimates are given for these moments as d = diam( D)→0. Physically, this means that ( k2+sup∣ q( x)) d2<1 and sup∣ q( x)∣ d< k. The found moments give an approximate position and the shape of the support of q. In particular, an ellipsoid D̃ and a real constant q̃ are found, such that the potential q̃ ( x) = q̃, x∈D̃, and q̃ ( x) = 0, x∉ D̃, produces the scattering data which fit best the observed scattering data and has the same zeroth, first, and second moments as the desired potential. A similar algorithm for finding the shape of D given only the modulus of the scattering amplitude A(α′,α) is also developed. 相似文献
2.
We consider the weakly singular boundary integral equation 𝒱 u = g on a randomly perturbed smooth closed surface Γ( ω) with deterministic g or on a deterministic closed surface Γ with stochastic g ( ω). The aim is the computation of the centered moments ℳ︁ k u, k ⩾ 1, if the corresponding moments of the perturbation are known. The problem on the stochastic surface is reduced to a problem on the nominal deterministic surface Γ with the random perturbation parameter κ ( ω). Resulting formulation for the k th moment is posed in the tensor product Sobolev spaces and involve the k -fold tensor product operators. The standard full tensor product Galerkin BEM requires 𝒪( Nk) unknowns for the k th moment problem, where N is the number of unknowns needed to discretize the nominal surface Γ. Based on [1], we develop the p -sparse grid Galerkin BEM to reduce the number of unknowns to 𝒪( N (log N) k –1) (cf. [2], [3] for the wavelet approach). (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
3.
Let n cells be arranged in a ring, or alternatively, in a row. Initially, all cells are unmarked. Sequentially, one of the unmarked
cells is chosen at random and marked until, after n steps, each cell is marked. After the kth cell has been marked the configuration of marked cells defines some number of islands: maximal sets of adjacent marked
cells. Let ξ
k
denote the random number of islands after k cells have been marked.
We give explicit expressions for moments of products of ξ
k
’s and for moments of products of 1/ξ
k
’s.
These are used in a companion paper to prove that if a random graph on the natural number is made by drawing an edge between i≧1 and j> i with probability λ/j, then the graph is almost surely connected if λ>1/4 and almost surely disconnected if λ≦1/4. 相似文献
4.
Summary Definitions of k-HNBUE and K-HNWUE are introduced and the relationship with other class of life distributions is studied. Various closure properties of k-HNBUE ( k-HNWUE) are proved. Finally bounds on the moments and survival function of k-HNBUE ( k-HNWUE) are given.
This research was supported by the ONR Grant N00014-78-C-0655. 相似文献
5.
We consider the asymptotics of certain symmetric k-tensors, the vector analogue of sample moments for i.i.d. random variables. The limiting distribution is operator stable as an element of the vector space of real symmetric k-tensors. 相似文献
6.
For a distribution function D we define its absolute and signed moments of order k∈ R, which generalise in a natural way the Hamburger moments of orders an even and an odd natural number. Similarly, for a real
function h we define its absolute and signed asymptotic means of order k∈ R. We show that if the means exist on an infinite and bounded set of values of k, then they exist on an interval I and coincide on I
o with the moments of D=D
h, the distribution function of the values of h, which is shown to exist (in the sense of Wintner). We also give a sufficient condition for D
h to be symmetric. These results apply to a class of functions h that contain in particular error terms related to the Euler phi function and to the sigma divisor function. A further application
on a certain class of converging trigonometrical series implies in particular classical results of A. Wintner establishing
the existence for such functions of a distribution function as well as Hamburger moments of arbitrarily large orders. The
remainder term of the prime number theorem belongs to this class provided the Riemann hypothesis holds, and the distribution
function of its values is shown to be “almost” symmetric. 相似文献
7.
Constants in the asymptotic formulae of E. M. Wright for the number of labeled connected graphs on n vertices and n − 1 + k edges ( k fixed) are shown to be moments of the mean distance from the origin in a certain restricted Brownian motion. © 1997 John Wiley & Sons, Inc. 相似文献
8.
This paper considers estimating parameters in the discrete distributions of order k such as the binomial, the geometric, the Poisson and the logarithmic series distributions of order k. It is discussed how to calculate maximum likelihood estimates of parameters of the distributions based on independent observations. Further, asymptotic properties of estimators by the method of moments are investigated. In some cases, it is found that the values of asymptotic efficiency of the moment estimators are surprisingly close to one. 相似文献
9.
Summary In a recent paper by A. P. Basu and N. Ebrahimi (1984, Ann. Inst. Statist. Math., A, 36, 87–100) a new class of life distributions
called k-HNBUE (with dual k-HNWUE) is introduced. Closure properties and bounds on the moments and on the survival function to a k-HNBUE ( k-HNWUE) life distribution are presented. However, some of the results presented are incorrect.
This research was supported by Swedish Natural Science Research Council Post Doctoral Fellowship F-PD 1564-100. 相似文献
10.
It is shown how mesh‐centered finite differences can be obtained from unconventional mixed‐hybrid nodal finite elements. The classical Raviart‐Thomas schemes of index k (RT k) are based on interpolation parameters that are cell and/or edge moments. For the unconventional form (URT k), they become point values at Gaussian points. In particular, the scheme URT1 is fully described. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2006 相似文献
11.
We consider the moment space Mn\mathcal{M}_{n} corresponding to p× p real or complex matrix measures defined on the interval [0,1]. The asymptotic properties of the first k components of a uniformly distributed vector ( S1,n, ... , Sn,n) * ~ U ( Mn)(S_{1,n}, \dots , S_{n,n})^{*} \sim\mathcal{U} (\mathcal{M}_{n}) are studied as n→∞. In particular, it is shown that an appropriately centered and standardized version of the vector ( S
1,n
,…, S
k,n
) ∗ converges weakly to a vector of k independent p× p Gaussian ensembles. For the proof of our results, we use some new relations between ordinary moments and canonical moments
of matrix measures which are of their own interest. In particular, it is shown that the first k canonical moments corresponding to the uniform distribution on the real or complex moment space Mn\mathcal{M}_{n} are independent multivariate Beta-distributed random variables and that each of these random variables converges in distribution
(as the parameters converge to infinity) to the Gaussian orthogonal ensemble or to the Gaussian unitary ensemble, respectively. 相似文献
12.
A continuous space/time approximation of the well known ‘directed polymer’ problem is considered. Connection between the ‘Helmholtz Free Energy’ and the ‘Two Walker problem’ is shown. Rigorous proof of the superdiffusive mean squared displacement exponent of 4/3 is given when there is one space dimension and one time dimension. Asymptotically diffusive behaviour of c( k) tis shown when there are one ‘time’ and two ‘space’ dimensions. For higher dimensions, the behaviour is diffusive and the mean squared displacement is asymptotically t d. These results hold for all temperature, because the phase transition in the discrete model is no longer present in the continuous model; the renormalization procedure has set the transition temperature to k crit =0The joint distribution is also shown to be asymptotically sub-Gaussian for all dimensions and all temperatures (in the sense that the p thmoments as a function of pincrease more slowly than the moments of a Gaussian distribution). The ‘Helmholtz Free Energy’ is also calculated for this model and the quenched and annealed free energies are shown to be identical for all temperature 相似文献
13.
This is a direct continuation of Part II of this series of papers and we shall not only improve (numerically) all our former
results in Part II, but also prove new theorems, Theorem 4 on the function f( t) = log Γ( t+λ) and Theorem 5 for k-th power moments, k = 2,...,7, by elaborating our previous arguments.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
14.
Summary This paper gives some results on calculation of probabilities and moments of the discrete distributions of order k. Further, a new distribution of order k, which is called the logarithmic series distribution of order k, is investigated. Finally, we discuss the meaning of the order of the distributions.
The Institute of Statistical Mathematics 相似文献
15.
In the separable Hilbert space ( H, ·, ·) the following “operator moment problem” is solved: given a complex sequence ( ck) k ε Z generated by a meromorphic function f, find T ε B( H) and u0 ε H such that Tku0, u0 = ck ( k ε Z). If the sequence ( ck) k ε Z is “normal,” an adapted form of Vorobyev's method of moments yields a sequence of two point Padé approximants to f. A sufficient condition for convergence of this sequence of approximants is given. 相似文献
16.
In this paper, we compute all the moments of the real Wishart distribution. To do so, we use the Gelfand pair ( S2k, H), where H is the hyperoctahedral group, the representation theory of H and some techniques based on graphs. 相似文献
17.
Summary The class of discrete distributions of order k is defined as the class of the generalized discrete distributions with generalizer a discrete distribution truncated at zero
and from the right away from k+1. The probability function and factorial moments of these distributions are expressed in terms of the (right) truncated
Bell (partition) polynomials and several special cases are briefly examined. Finally a Poisson process of order k, leading in particular to the Poisson distribution of order k, is discussed. 相似文献
18.
Summary Consider the set of proper probability distributions on the nonnegative integers having the first k moments (fixed) in common. It is desired to find the element of this set whose corresponding probability generating function (p.g.f.) lies entirely above or below the others. Using convexity arguments, it is shown that the extremal distribution exists, is unique, and is necessarily an element of a certain subclass of the class of all ( k + 1)-point distributions. This subclass is entirely characterized by the geometrical properties of its set of support. The alternation of upper and lower bounds with the parity of k is also explained. There is mention of how the techniques developed here apply to more general discrete optimization problems, and the connection with the theory of cyclic polytopes is also discussed.This work was partially supported by Army Research Office Grant #DAHCO 04-74-G-0178 awarded to the Department of Statistics, Princeton University 相似文献
19.
We show for the M/G/1 processor sharing queue that the service time distribution is regularly varying of index -ν, ν non-integer,
iff the sojourn time distribution is regularly varying of index -ν. This result is derived from a new expression for the Laplace–Stieltjes
transform of the sojourn time distribution. That expression also leads to other new properties for the sojourn time distribution.
We show how the moments of the sojourn time can be calculated recursively and prove that the kth moment of the sojourn time is finite iff the kth moment of the service time is finite. In addition, we give a short proof of a heavy traffic theorem for the sojourn time
distribution, prove a heavy traffic theorem for the moments of the sojourn time, and study the properties of the heavy traffic
limiting sojourn time distribution when the service time distribution is regularly varying. Explicit formulas and multiterm
expansions are provided for the case that the service time has a Pareto distribution.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
20.
We consider a general k-dimensional discounted infinite server queueing process (alternatively, an incurred but not reported claim process) where the multivariate inputs (claims) are given by a k-dimensional finite-state Markov chain and the arrivals follow a renewal process. After deriving a multidimensional integral equation for the moment-generating function jointly to the state of the input at time t given the initial state of the input at time 0, asymptotic results for the first and second (matrix) moments of the process are provided. In particular, when the interarrival or service times are exponentially distributed, transient expressions for the first two moments are obtained. Also, the moment-generating function for the process with deterministic interarrival times is considered to provide more explicit expressions. Finally, we demonstrate the potential of the present model by showing how it allows us to study semi-Markovian modulated infinite server queues where the customers (claims) arrival and service (reporting delay) times depend on the state of the process immediately before and at the switching times. 相似文献
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