Convergence of Appell Polynomials of Long Range Dependent Moving Averages in Martingale Differences

We study limit distribution of partial sums S_N,k(t) = _{s = 1} ^{[N t]} A_k(X_s) of Appell polynomials of the long-range dependent moving average process X_t> = _{i t} b_{t - i i}, where {_i} is a strictly stationary and weakly dependent martingale difference sequence, and b_i i^{d - 1} (0 < d < 1/2). We show that if k(1-2 d)<1, then suitably normalized partial sums S_N,k(t) converge in distribution to the kth order Hermite process. This result generalizes the corresponding results of Surgailis, and Avram and Taqqu obtained in the case of the i.i.d. sequence { _i}.     

Local structure and triplet energy migration in p-dichlorobenzene-p-dibromobenzene solid solutions

Studies of the first triplet absorption and emission spectra of p-dichlorobenzene-p-dibromobenzene (DCB-DBB) mixed crystals agree generally with the data, indicating that this system forms solid solutions. However, the spectral properties are found to be very different from that of isotopically mixed crystals of comparable concentrations. The singlet-triplet absorption spectra of the DCB-DBB mixtures are generally broad and not amenable to detailed analysis indicating significant site dependent perturbations of the DCB and DBB triplet energies. Energy migration enhances emission from the lower energy sites and in consequence a red shift in the position of the emission (0,0) is observed, which is a maximum at equimolar concentrations. The emission bands are generally much broader than found for isotopically mixed crystals, indicating that the many types of sites in the DCB-DBB system remained uncoupled. This is a direct consequence of exciton trapping by inhomogeneous energy broadening caused by the site energy disorder being greater than the triplet exciton band width. Long-range triplet energy migration is not observed at DCB concentrations less than 99 per cent. This high limit is only expected for near one-dimension energy migration topologies. New structure observed at low DCB concentrations is tentatively interpreted as being due to the formation of DCB n-mers. The observed splittings indicate that the gas-to-crystal shift of the DCB T ₁ state increases (becomes more negative) by 11 cm^-1 when a neighbouring DBB molecule is replaced by DCB.     

A note on the elusive 1E2g state in the two-photon spectrum of benzene

An intense, broad feature appears in both two-photon thermal lens and multiphoton ionization spectra of liquid benzene in the 2000–1800 A region. Such bands in liquids of low ionization potential are argued to be direct two-photon excitations into the conduction bands of the liquids, appearing three or more eV below the gas-phase thresholds due to strong solvation of the ionic states. An earlier assignment of the feature in liquid benzene as a transition to the ¹E_2g valence state seems unlikely.     

Effect of AlF3 production waste on the processes of hydration and hardening of the alkali-activated Portland cement with sodium silicate hydrate

Journal of Thermal Analysis and Calorimetry - Generally, the early strength of hardened Portland cement paste is controlled, by changing the mineral composition of clinker and grinding fineness. By...     

The Estimation of Parameters for the Tapered Pareto Distribution from Incomplete Data

Lithuanian Mathematical Journal - In this paper, we consider estimation of unknown parameters of the tapered Pareto distribution, which belongs to the class of semiheavy distributions, by a sample...     

The increment ratio statistic

We introduce a new statistic written as a sum of certain ratios of second-order increments of partial sums process of observations, which we call the increment ratio (IR) statistic. The IR statistic can be used for testing nonparametric hypotheses for d-integrated () behavior of time series X_t, including short memory (d=0), (stationary) long-memory and unit roots (d=1). If S_n behaves asymptotically as an (integrated) fractional Brownian motion with parameter , the IR statistic converges to a monotone function Λ(d) of as both the sample size N and the window parameter m increase so that N/m→∞. For Gaussian observations X_t, we obtain a rate of decay of the bias EIR-Λ(d) and a central limit theorem (N/m)^1/2(IR-EIR)→N(0,σ²(d)), in the region . Graphs of the functions Λ(d) and σ(d) are included. A simulation study shows that the IR test for short memory (d=0) against stationary long-memory alternatives has good size and power properties and is robust against changes in mean, slowly varying trends and nonstationarities. We apply this statistic to sequences of squares of returns on financial assets and obtain a nuanced picture of the presence of long-memory in asset price volatility.     

Femtosecond real-time probing of transition state dynamics in a surface photoreaction: methyl desorption from CH3I on MgO(100)

A novel experimental approach to the investigation of surface adsorbate reaction dynamics is presented. The direct time-resolved monitoring of the surface reaction transition state and product formation dynamics were accomplished via pump-probe mass spectrometry. As an example, methyl iodide molecules adsorbed at submonolayer coverage on an ultrathin magnesia film on Mo(100) were photoexcited to the A-band by ultrafast laser pulse irradiation. Employing time-delayed multiphoton ionization the dynamics of the dissociative methyl iodide transition state and of the emerging methyl photoproduct could be detected with femtosecond resolution. The reaction times deduced from the temporal evolution of the methyl ion mass signal indicate a strong interaction of the methyl fragment with the substrate surface prior to desorption.     

Experimental and theoretical study of the OH vibrational spectra and overtone chemistry of gas-phase vinylacetic acid

In this study we present the gas-phase vibrational spectrum of vinylacetic acid with a focus on the nu = 1-5 vibrational states of the OH stretching transitions. Cross sections for nu = 1, 2, 4 and 5 of the OH stretching vibrational transitions are derived on the basis of the vapor pressure data obtained for vinylacetic acid. Ab initio calculations are used to assist in the band assignments of the experimental spectra, and to determine the threshold for the decarboxylation of vinylacetic acid. When compared to the theoretical energy barrier to decarboxylation, it is found that the nu OH = 4 transition with thermal excitation of low frequency modes or rotational motion and nu OH = 5 transitions have sufficient energy for the reaction to proceed following overtone excitation.