Asymptotic results for weighted means of linear combinations of independent Poisson random variables

ABSTRACT

In this paper we prove the large deviation principle for a class of weighted means of linear combinations of independent Poisson distributed random variables, which converge weakly to a normal distribution. The interest in these linear combinations is motivated by the diffusion approximation in Lansky [On approximations of Stein's neuronal model, J. Theoret. Biol. 107 (1984), pp. 631–647] of the Stein's neuronal model (see Stein [A theoretical analysis of neuronal variability, Biophys. J. 5 (1965), pp. 173–194]). We also prove an analogue result for sequences of multivariate random variables based on the diffusion approximation in Tamborrino, Sacerdote, and Jacobsen [Weak convergence of marked point processes generated by crossings of multivariate jump processes. Applications to neural network modeling, Phys. D 288 (2014), pp. 45–52]. The weighted means studied in this paper generalize the logarithmic means. We also investigate moderate deviations.     

Superposition of large butt-end and coaxial torsional and axial shear deformations of homogeneous and fiber-reinforced thick-wall cylinders

A mathematical model of superposition of large butt-end and coaxial torsional and axial shear deformations of homogeneous and fiber-reinforced thick-wall cylinders is constructed. The macroscopic stresses of the reinforced material are additively determined by matrix stresses and by tensile or constrained compression stresses in the reinforcing fibers. The model is based on the numerical solution of two boundary-value problems, one of which corresponds to the butt-end torsion and the other to the coaxial torsion and axial shear. The boundary-value problem on joint deformations is solved with the use of the displacement field determined from the solution to the boundary-value problem on butt-end torsion. The results obtained by applying this method to homogeneous and axially-radially reinforced thick-wall cylinders subjected to butt-end torsion with subsequent coaxial torsion and axial shear are presented. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 4, pp. 465–492, July–August, 2007.     

Structure of Positive Solutions of Quasilinear Elliptic Equations with Critical and Supercritical Growth

The structure of positive radial solutions to a class of quasilinear elliptic equations with critical and supercritical growth is precisely studied. A large solution and a small solution are obtained for the equations. It is shown that the large solution is unique, its asymptotic behaviour and flat core are also discussed.     

Simulation of the inherent turbulence and wake interaction inside an infinitely long row of wind turbines

The turbulence in the interior of a wind farm is simulated using large eddy simulation and the actuator line technique implemented in the Navier–Stokes equations. The simulations are carried out for an infinitely long row of turbines simulated by applying cyclic boundary conditions at the inlet and outlet. The simulations investigate the turbulence inherent to the wind turbines as no ambient turbulence or shear is added to this idealised case. The simulated data give insight into the performance of the wind turbines operating in the wake of others as well as details on key turbulent quantities. One of the key features of wakes behind wind turbines is the dynamic wake meandering, which is shown to be related to the wind turbine spacing and the vortex shedding from the turbine as a bluff body. The flow is analysed and reconstructed by applying proper orthogonal decomposition.     

大平面二极管虚阴极振荡器的宽脉冲微波辐射

给出了产生宽脉冲微波辐射的大平面天鹅绒二极管虚阴极振荡器的结构和测试装置,测得了二极管中阴–阳极等离子体的闭合速率为30~43km/s,获得了微波辐射的最大脉宽为1.5μs,产生的微波峰值功率约为15MW,频率为0.5GHz,指出这种平面二极管型虚阴极振荡器在辐射脉宽,辐射频率和辐射功率三者之间存在着物理上的制约关系,认为同轴型虚阴极振荡器是突破这种制约关系的一个新途径。     

An economic model for investing in sulfur oxide control technology development

The model estimates, subject to restrictions, the functional relationship between national sulfur dioxide discharges and investment in control technology development. Estimates may be made for different product demands, allowed cost increases, and clean fuel availabilities. Control technology development may be accelerated by increased investment. Both optimal and sub-optimal solutions are calculated for an example problem. A general computing method is provided.The model was presented at the Industrial Process Design for Pollution Control Workshop, Chicago, Illinois, Oct. 1973; copyright released by the American Institute of Chemical Engineers for publication for the first time in the monographNormative Analysis in Policy Decisions: Public and Private.     

Assessing the subsequent effect of nitrogen released from tobacco-waste on maize crop using a 15N isotope technique

The investigation of the residual effect of nitrogen (N) released from tobacco-waste (TW) using isotope techniques will provide valuable data for sustainable organic farming. For this aim, a pot experiment was conducted using the ¹⁵N isotope technique. The experiment was based on a completely randomised design with four replications and was conducted on a calcareous ustochrepts soil. TW at levels of 0, 10, 20, 30 and 40 t ha^?1 and N fertiliser as (NH₄)₂SO₄ at levels of 0, 20, 40, 60 and 80 kg N ha^?1 were used for the Bezostaja-1 wheat variety. Concerning mineral N fertilisation with 20 and 80 kg N ha^?1, additional treatments with ¹⁵N-labelled (NH₄)₂SO₂ (10 at.% exc.) have been applied. Following harvesting wheat plants, the Pioneer 3377 maize variety was used to see the residual effect of TW. After harvesting, dry matter yields were recorded and total N concentrations were determined. ¹⁵N determinations and calculations were also made for ¹⁵N treatments separately. TW had a significant residual effect on the growth of corn plant under the pot condition. Increasing rates of TW significantly increased the dry matter yield of corn plant following wheat from 3.31 t ha^?1 (at control) to 7.89 t ha^?1 (at the TW treatment of 40 t ha^?1). The ¹⁵N values derived from the ¹⁵N fertiliser decreased with increasing TW application. The average values of N derived from N fertiliser (Ndff) varied from 2.14 to 3.09% at the rates of 20 and 80 kg N ha^?1, respectively. However, N derived from TW (Ndftw) significantly increased from 16.93 to 24.59% (at 20 kg N ha^?1), and it also increased from 23.06 to 28.15% (at 80 kg N ha^?1) with increasing TW applications from 20 to 40 t ha^?1, respectively.     

Derivation of macroscopic equations for individual cell‐based models: a formal approach

In this paper we review the theory of cells (particles) that evolve according to a dynamics determined by friction and that interact between themselves by means of suitable potentials. We derive by means of elementary arguments several macroscopic equations that describe the evolution of cell density. Some new results are also obtained—a formal derivation of a limit equation in the case of attractive potential as well as in the case of repulsive potential with a hard‐core part are presented. Finally we discuss the possible relevance of those results within the framework of individual cell‐based models. Several classes of potentials, including hard‐core, repulsive and potentials with attractive parts are discussed. The effect of noise terms in the equation is also considered. Copyright © 2005 John Wiley & Sons, Ltd.     

Impact of Linear Operator on the Convergence of HAM Solution: A Modified Operator Approach

The linear operator plays an important role in the computational process of Homotopy Analysis Method (HAM). In HAM frame any kind of linear operator can be chosen to develop a solution. Hence, it is easy to introduce the modified/physical parameter dependent linear operators. The effective use of these operators has been judged through solving fluid flow problems. Modification in linear operators affects the solution and improves the computational efficiency of HAM for larger values of parameters. The convergence rate of the solution is rapid and several times higher resulting in less computational time.     

B-值随机变量序列大数定律的收敛速度

设{X_n:n≥1}是在某可分Banach空间B上取值的独立随机变量序列,S_n=X_1+…+X_n,n≥1,对某00和>1,定义P_n(ε)=P(‖S_n‖/n~(1/p)≥ε)。本文的目的是研究当n→+∞时,P(ε)→0的速度,在Banach空间上推广了Heyde和Rohatgi的结果;同时,本文还讨论了P_n(ε)→0的速度与S_n/n~(1/p)→0 a.s.的关系问题。