Monitoring changes in the error distribution of autoregressive models based on Fourier methods

We develop a procedure for monitoring changes in the error distribution of autoregressive time series while controlling the overall size of the sequential test. The proposed procedure, unlike standard procedures which are also referred to, utilizes the empirical characteristic function of properly estimated residuals. The limit behavior of the test statistic is investigated under the null hypothesis as well as under alternatives. Since the asymptotic null distribution contains unknown parameters, a?bootstrap procedure is proposed in order to actually perform the test and corresponding results on the finite?Csample performance of the new method are presented. As it turns out the procedure is not only able to detect distributional changes but also changes in the regression coefficient.     

Calculations on endohedral C74 complexes

While empty C74 is still a rather elusive fullerene, its endohedral derivatives are well established. The report surveys computations for three of C74-based endohedrals--Ca@C74, Ba@C74, and Yb@C74. A set of six C74 cages is considered, namely one cage with isolated pentagons, three isomers with a pentagon-pentagon junction, two structures with one pair of connected pentagons, and one heptagon. Special interest is paid to the Gibbs-energy evaluations for estimations of the relative populations.     

Angular Spectrum of Phase-conjugate Field Generated in Four-wave Mixing

Abstract

The phase-conjugate mirror realized by means of degenerate four-wave mixing in a Kerr-like medium is investigated using the angular spectrum representation of interacting fields. The analysed model is based on the nonlinear mixing of two infinite plane pump waves with the spatially limited probe and signal waves. Relations among harmonic components of the probe and signal fields are derived assuming non-depleted pumping and neglecting the evanescent waves. The influence of the injected signal field on the frequency spectrum of the generated phase-conjugate field is also examined.     

Consequences of diffusion theory for shrinkage of concrete

The paper reviews the known consequences of diffusion theory for the mathematical modelling of shrinkage, including the size dependence of drying half-time, and the initial and final asymptotic shapes of the time curves of total moisture loss, to which shrinkage is proportional. The mathematical arguments are extended and presented with greater rigour and generality than before, taking the non-linearity of the diffusion equation as well as ageing into account.     

Fast algorithm for nonparametric arbitrage-free SPD estimation

State price density (SPD) contains important information concerning market expectations. An estimator of the SPD based on observed European option prices, taking into account the time of the trade, has been previously considered. Financial markets produce huge amounts of data and, due to time constraints, it is not always possible to calculate the estimator using all available data. Using a model for the covariance structure of the observed option prices, the algorithm identifies observations with little importance to the estimator. Dropping these observations increases the speed of computation and allows frequenter updating of the estimator. The algorithms efficiently use indices that combine information contained in the data. Fast algorithms are proposed and their properties are investigated using both simulated and real data sets.     

Micropore structure analysis of coal from adsorption isotherms of methanol

Results are presented of a study of the distribution of pore volume and surface in micropores of coal from adsorption equilibria of methanol vapours at temperatures ranging between 293 and 343 K according to a new method. Typical parameters of the micropore structure of twenty samples of coals of carbon contents between 64 and 91% are calculated for a model of cylindrical pores. The micropore surface areas are compared with the results obtained by using the DKR and BET equations, and with already published data from small-angle X-ray scattering. The agreement between results is satisfactory. This evidence suggests that the use of the new method of evaluating the basic parameters of the microstructure can be recommended.     

Critical evaluation of sequential extraction and sink-float methods used for the determination of Ga and Ge affinity in lignite

The affinities of Ga and Ge in lignite were determined using sequential extraction (SE) and element affinity calculation (EAC) based on sink-float data. For this study a bulk lignite sample was fractioned into two sets. The first set of samples (A) consisted of the different grain sizes fractions; the second one set (B) was prepared by density fractionation. Sequential extractions [1] were performed on both sets of fractions with very good agreement between determined organic elements affinities (OEA of Ga evaluated from A data is 32%, from B data 35%; OEA of Ge evaluated from A data is 31% and from B data 26%). The data of B lignite fractions were evaluated using two element affinity calculations: (a) EAC (I) of Klika and Kolomazník [2] and b) newly prepared subroutine EAC (II) based on quantitative contents of lignite macerals and minerals. There was also good agreement between both methods obtained (OEA of Ga calculated by EAC (I) is 83% and by EAC (II) 77%; OEA of Ge calculated by EAC (I) is 89% and by EAC (II) 97%). The significant differences of organic elements affinities of Ga and Ge evaluated by sequential extraction and by element affinity calculation based on sink-float data are discussed.     

Hydraulic formulae for the added masses of an impermeable sphere moving near a plane wall

Simple formulae for the components of the added-mass coefficient tensor of a sphere moving near a wall with variable velocity in an ideal fluid bounded by a solid surface are derived. The added mass is calculated numerically as a function of the dimensionless distance between the sphere and the wall for both perpendicular and parallel motions. The calculation is performed by the method of successive images. The velocity field is computed as the sum of the velocity fields of sequences of dipoles located along the axis. The obtained dependences of the added-mass tensor components are fitted by simple continuous functions with high accuracy.