Gr\"obner-Shirshov bases for Lie algebras over a commutative algebra

In this paper we establish a Gr\"{o}bner-Shirshov bases theory for Lie algebras over commutative rings. As applications we give some new examples of special Lie algebras (those embeddable in associative algebras over the same ring) and non-special Lie algebras (following a suggestion of P.M. Cohn (1963) \cite{Conh}). In particular, Cohn's Lie algebras over the characteristic $p$ are non-special when $p=2,\ 3,\ 5$. We present an algorithm that one can check for any $p$, whether Cohn's Lie algebras is non-special. Also we prove that any finitely or countably generated Lie algebra is embeddable in a two-generated Lie algebra

Modelisation pour l'evaluation de ratard dans les structures CMOS : algorithmes et exemples

SIGLECNRS T Bordereau / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

Monitoring of Indoor Farming of Lettuce Leaves for 16 Hours Using Electrical Impedance Spectroscopy (EIS) and Double-Shell Model (DSM)

An electrical impedance spectroscopy (EIS) experiment was performed using a double-shell electrical model to investigate the feasibility of detecting physiological changes in lettuce leaves over 16 h. Four lettuce plants were used, and the impedance spectra of the leaves were measured five times per plant every hour at frequencies of 500 Hz and 300 kHz. Estimated R-C parameters were computed, and the results show that the lettuce leaves closely fit the double-shell model (DSM). The average resistance ratios of R1 = 10.66R4 and R1 = 3.34R2 show high resistance in the extracellular fluid (ECF). A rapid increase in resistance (R1, R2, and R4) and a decrease in capacitance (C3 and C5) during water uptake were observed. In contrast, a gradual decrease in resistance and an increase in capacitance were observed while the LED light was on. Comparative studies of leaf physiology and electrical value changes support the idea that EIS is a great technique for the early monitoring of plant growth for crop production