Pumping lemmas are created to prove that given languages are not belong to certain language classes. There are several known pumping lemmas for the whole class and some special classes of the context-free languages. In this paper we prove new, interesting pumping lemmas for special linear and context-free language classes. Some of them can be used to pump regular languages in two place simultan...

Recently a distributed Bragg reflection (DBR) laser diode was commercialised by SDL (USA) for helium optical pumping experiments. An interesting feature of the new device is the possibility of frequency modulation of the diode output by modulating the current intensity, leading to a new pumping scheme called optical pumping with frequency modulated light. We develop this method to induce spin p...

Experiments illustrating advantages and unique features of double-resonance and optical pumping on electromagnetically confined, laser-cooled ions are discussed. In certain cases, scattered light from the cooling transition can be used as a monitor in double-resonance experiments to give nearly 100% detection efficiency. Nonradiative relaxation rates are extremely small for stored ions, permitt...

Pumping stations play an important role in agriculture development projects. Performance of the pumping stations should satisfy water requirements, and management. There are many problems face these pumping stations affecting their reliability and stability. Hydraulic problems are the most important item in the field of pumping station operation and design. Motivation of this research was prese...

Context. The turbulent pumping effect corresponds to the transport of magnetic flux due to the presence of density and turbulence gradients in convectively unstable layers. In the induction equation it appears as an advective term and for this reason it is expected to be important in the solar and stellar dynamo processes. Aims. In this work, we have explored the effects of the turbulent pumpin...

Detecting and quantifying small drawdown at observation wells distant from the pumping well greatly expands the characterized aquifer volume. However, this detection is often obscured by water level fluctuations such as barometric and tidal effects. A reliable analytical approach for distinguishing drawdown from nonpumping water-level fluctuations is presented and tested here. Drawdown is disti...

Head measurements at a single observation well during a cross-hole pumping test carry a great amount of information about aquifer heterogeneity other than the average property of the aquifer as implied in Theis analysis of aquifer test. In this commentary, we use simple examples and a probabilistic reasoning approach based on Darcy’s law to unravel this information, buried in the results of qua...

An analytical solution for the case of transient, pumping-induced drawdown in a nonuniform aquifer is presented. The nonuniform aquifer is conceptualized as a uniform matrix into which a disk of anomalous properties has been placed. The disk can be arbitrarily located with respect tothe pumping well. This solution can be used to develop considerable insight concerning the nature of drawdown i n...

Insects that are small or exhibit low metabolic rates are considered to not require active ventilation to augment diffusive gas exchange. Some pupae with low metabolic rates exhibit abdominal pumping, a behaviour that is known to drive tracheal ventilation in the adults of many species. However, previous work on pupae suggests that abdominal pumping may serve a non-respiratory role. To study th...