On lacunary statistical convergence of order α

In this article, we introduce the concept of lacunary statistical convergence of order α of real number sequences and give some inclusion relations between the sets of lacunary statistical convergence of order α and strong N_θ^α(p)-summability. Furthermore, some relations between the spaces N_θ^αS_θ^α are examined.     

Ultrafast temperature jump in liquid water studied by a novel infrared pump-x-ray probe technique

We report the first infrared pump-x-ray probe study of the structural dynamics of liquid water. Femtosecond infrared excitation via the O–H stretching band induces an ultrafast temperature jump that gives rise to changes in the hydrogen bond network. Such changes are probed via the transient x-ray absorption at the oxygen K edge using 70 ps x-ray pulses from a storage ring source. We measure spectra and time evolution of the transient x-ray absorption and calibrate the absolute change of temperature. Our work paves the way for future studies with femtosecond x-ray probe pulses.