Changes of the solution pH due to exposure by high-voltage electric pulses

The change of the pH of a NaCl solution (139-149 mM NaCl) buffered with 5-15 mM sodium phosphates (pH 7.4) during electromanipulation was studied. It has been determined that an increase in the pH value of electroporation solution of a whole chamber volume, caused by the application of electric field pulses, commonly used in cell electromanipulation procedures, can exceed 1-2 pH units. Several materials for the cathode were tested. In all cases a stainless steel anode was utilized. The aluminum cathode gave a two-fold greater DeltapH in comparison with platinum, copper or stainless steel cathodes. In addition, a substantial release of aluminum (up to 1 mg/l) from the cathode was observed. It has also been found that the shift in pH depended on the medium conductivity: DeltapH of the solution, in which sucrose was substituted for NaCl, was about 5 times less. On the basis of the results obtained here, to avoid the plausible undesirable consequences of the cathodic electrolysis processes, in particular under the conditions of strong electric treatment, it could be recommended that chambers with aluminum electrodes not be utilized and one should use strongly buffered solutions of low conductivity and alternating current (sine or square wave) bipolar electric pulses.     

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}.     

A two-sample test for comparison of long memory parameters

We construct a two-sample test for comparison of long memory parameters based on ratios of two rescaled variance (V/S) statistics studied in Giraitis et al. [L. Giraitis, R. Leipus, A. Philippe, A test for stationarity versus trends and unit roots for a wide class of dependent errors, Econometric Theory 21 (2006) 989-1029]. The two samples have the same length and can be mutually independent or dependent. In the latter case, the test statistic is modified to make it asymptotically free of the long-run correlation coefficient between the samples. To diminish the sensitivity of the test on the choice of the bandwidth parameter, an adaptive formula for the bandwidth parameter is derived using the asymptotic expansion in Abadir et al. [K. Abadir, W. Distaso, L. Giraitis, Two estimators of the long-run variance: beyond short memory, Journal of Econometrics 150 (2009) 56-70]. A simulation study shows that the above choice of bandwidth leads to a good size of our comparison test for most values of fractional and ARMA parameters of the simulated series.     

Nonparametric estimation of the local Hurst function of multifractional Gaussian processes

A new nonparametric estimator of the local Hurst function of a multifractional Gaussian process based on the increment ratio (IR) statistic is defined. In a general frame, the point-wise and uniform weak and strong consistency and a multidimensional central limit theorem for this estimator are established. Similar results are obtained for a refinement of the generalized quadratic variations (QV) estimator. The example of the multifractional Brownian motion is studied in detail. A simulation study is included showing that the IR-estimator is more accurate than the QV-estimator.     

Effect of pozzolanic waste materials on hydration peculiarities of Portland cement and granulated expanded glass-based plaster

Journal of Thermal Analysis and Calorimetry - The article analyses the peculiarities of the combined effect on hydration process of the following pozzolanic additives: metakaolin waste (MW),...     

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.     

Aggregation of random-coefficient AR(1) process with infinite variance and common innovations

We discuss aggregation of random-coefficient AR(1) processes X _i,t = a _i X _i,t?1 + ε _t , i = 1,…,N, with i.i.d. coefficients a _i ∈ (?1, 1) and common i.i.d. innovations {ε _t } belonging to the domain of attraction of an α-stable law (0 < α ≤ 2). Particular attention is given to the case of slope coefficient having probability density growing regularly to infinity at points a = 1 and a = ?1. We obtain conditions under which the limit aggregate \( {\bar X_t} = {\lim_{N \to \infty }}{N^{ - 1}}\sum\nolimits_{i = 1}^N {{X_{i,t}}} \) exists and exhibits long memory in a certain sense. In particularly, we show that suitably normalized partial sums of the \( {\bar X_t} \)’s tend to a fractional α-stable motion and that \( \left\{ {{{\bar X}_t}} \right\} \) satisfies the long-range dependence (sample Allen variance) property of Heyde and Yang. We also extend some results of Zaffaroni from the finite variance case to the infinite variance case.     

Invariance principle for a class of non stationary processes with long memory

We prove a functional central limit theorem for the partial sums of a class of time varying processes with long memory. To cite this article: A. Philippe et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).