Fractionally differenced models for water quality time series

This paper deals with the selection and evaluation of statistical techniques for use in the modeling and forecasting of water quality time series. The focus is on statistical concepts relevant to the analysis of flows and concentrations. A selection of time series procedures has been used for auditing water quality archival data, including the screening of data sets, correlation and spectrum calculations, and iterative model fitting. A summary is provided of experience with analyzing archival data on the Niagara River and the use of a fractionally differenced model.This paper is the result of a study performed for the International Joint Commission, United States and Canada. The authors gratefully acknowledge the direction and support provided by Dr. Joel L. Fisher.     

Analytical and approximate solutions of(2+1)-dimensional time-fractional Burgers-Kadomtsev-Petviashvili equation

In this paper, we applied the sub-equation method to obtain a new exact solution set for the extended version of the time-fractional Kadomtsev-Petviashvili equation, namely BurgersKadomtsev-Petviashvili equation(Burgers-K-P) that arises in shallow water waves.Furthermore, using the residual power series method(RPSM), approximate solutions of the equation were obtained with the help of the Mathematica symbolic computation package. We also presented a few graphical illustrations for some surfaces. The fractional derivatives were considered in the conformable sense. All of the obtained solutions were replaced back in the governing equation to check and ensure the reliability of the method. The numerical outcomes confirmed that both methods are simple, robust and effective to achieve exact and approximate solutions of nonlinear fractional differential equations.     

Na原子链表面等离激元特性的含时密度泛函研究

本文用含时密度泛函理论研究了线性Na原子链的表面等离激元机理.主要在原子尺度下模拟计算了体系随着原子数增加及原子间距变化的集体激发过程.研究发现线性原子链有一个普遍的特性——存在一个纵模和两个横模.两个横模一般在实验上很难被观测到.纵模随着原子链长度增加,能量红移的同时,该纵模主峰的强度呈线性增长.随着原子个数的增加,端点模式(TE)开始蓝移,能量和偶极强度都逐渐趋向饱和.横模能量被劈裂的原因概括如下:(一)每个位置的电子受到的势不同,在两端的电子受到的势要比在中间的电子受到的势要高,因此两端的电荷积累也比中间多;(二)端点存在悬挂键,所以中间的电子-电子间相互作用与端点的不一样,这两方面又都与原子间距d有关.     

Singularly perturbed nonlinear second order elliptic equation

In this paper, we study singular perturbation problems of some semi-linear second order elliptic equations with nonlinear boundary value conditions: where ε is a small positive parameter and u/ l is a directional derivative, which lies on an oblique vector (x,ε). We have given a construction of the asymptotic solutions and proof of their asymptotic correctness, which is based on the principle of contraction mapping.     

Spontaneous magnetization of the Ising model on a 4–8 lattice

The spontaneous magnetization of the Ising model on a 4–8 lattice with six different coupling constants and two different magnetic moments is studied. A formula for the spontaneous magnetization is proposed. The result agrees with the exact low-temperature series expansions up to the 12th order.     

On the summation of the Brillouin-Wigner type perturbation series

It is shown that if the ‘mean excitation energy’ assumption is introduced in the Brillouin-Wigner perturbation series, then the resulting series can be exactly summed. The implications of the result for calculating energy shift and for constructing trial functions are examined with special reference to the ground state of the helium atom.     

Exact expressions for row correlation functions in the isotropicd=2 ising model

We present exact explicit expressions for the row spin-spin correlation functions _{00 n}0 in the isotropicd= 2 Ising model, in terms of elliptic integrals, forn 5. We also give a general structural formula for _{00 n}0.     

Molecular dynamics calculations of the hard-sphere equation of state

The equation of state of the hard-sphere fluid is studied by a Monte Carlomolecular dynamics method for volumes ranging from 25V ₀ to 1.6V ₀ , whereV ₀ is the close-packed volume, and for system sizes from 108 to 4000 particles. TheN dependence of the equation of state is compared to the theoretical dependence given by Salsburg for theNPT ensemble, after correction for the ensemble difference, in order to obtain estimates for the thermodynamic limit. The observed values of the pressure are compared with both the [3/2] and the [2/3] Padé approximants to the virial series, using Kratky's value for the fifth virial coefficientB ₅ and choosingB ₆ andB ₇, to obtain a least-squares fit. The resulting values ofB ₆ andB ₇ lie within the uncertainties of the Ree-Hoover-Kratky Monte Carlo estimates for these virial coefficients. The values ofB ₈,B ₉, andB ₁₀ predicted by our optimal [3/2] approximant are also reported. Finally, the Monte Carlo-molecular dynamics equation of state is compared with a number of analytic expressions for the hard-sphere equation of state.Work supported by the Office of Basic Energy Sciences, U.S. Department of Energy.     

The application of Hölder exponent to traffic congestion warning

In this paper, we applied multifractal modeling techniques to analyze the traffic data collected from the Beijing Yuquanying. The results indicated that multifractal characteristics obviously exist in the traffic system; the degree of fractality of these traffic data tends to increase as the traffic system becomes congested; the Hölder exponent that measures the local rate of fractality may be used as indicators to predict the presence of the traffic congestion.     

Factorizing multivariate time series operators

Motivated by problems occurring in the empirical identification and modelling of a n-dimensional ARMA time series X(t) we study the possibility of obtaining a factorization (I + a₁B + … + a_pB^p) X(t) = [Π_i=1^p (I ? α_iB)] X(t), where B is the backward shift operator. Using a result in [3] we conclude that as in the univariate case such a factorization always exists, but unlike the univariate case in general the factorization is not unique for given a₁, a₂,…, a_p. In fact the number of possibilities is limited upwards by $\text{(np)!}\text{(n!)}{}^{\mathrm{p}}$, there being cases, however, where this maximum is not reached. Implications for the existence and possible use of transformations which removes nonstationarity (or almost nonstationarity) of X(t) are mentioned.