Hybrid analysis of nonlinear circuits: DAE models with indices zero and one

We extend in this paper some previous results concerning the differential-algebraic index of hybrid models of electrical and electronic circuits. Specifically, we present a comprehensive index characterization which holds without passivity requirements, in contrast to previous approaches, and which applies to nonlinear circuits composed of uncoupled, one-port devices. The index conditions, which are stated in terms of the forest structure of certain digraph minors, do not depend on the specific tree chosen in the formulation of the hybrid equations. Additionally, we show how to include memristors in hybrid circuit models; in this direction, we extend the index analysis to circuits including active memristors, which have been recently used in the design of nonlinear oscillators and chaotic circuits. We also discuss the extension of these results to circuits with controlled sources, making our framework of interest in the analysis of circuits with transistors, amplifiers, and other multiterminal devices.

Seven Ulmus minor clones tolerant to Ophiostoma novo-ulmi registered as forest reproductive material in Spain

The Spanish elm programme began in 1986 in response to the devastating impact of Dutch elm disease on natural elm stands and urban trees. Its main objectives were to conserve remaining genetic resources and select and breed tolerant native elm genotypes. After 27 years of work conducting susceptibility trials on thousands of elm genotypes, the first seven tolerant Ulmus minor trees are now being registered by the Spanish Environmental Administration. This paper presents the results of the susceptibility tests on these clones and their distinctive genetic, morphological and phenological features. In all susceptibility trials the commercial ?Sapporo Autumn Gold? clone, which is highly tolerant to O. novo-ulmi, was used as a control. The registered clones were named ?Ademuz?, ?Dehesa de la Villa?, ?Majadahonda?, ?Toledo?, ?Dehesa de Amaniel?, ?Retiro? and ?Fuente Umbría?. The most tolerant clone was ?Dehesa de Amaniel?, as its wilting values were below 5% during the two consecutive inoculation trials performed in Madrid. ?Fuente Umbría?, tested over four consecutive years in Guadalajara and Palencia, was the Spanish clone with the most reliable tolerance level to O. novo-ulmi. The ?Ademuz? and ?Majadahonda? clones had the highest ornamental scores and are promising trees for use in urban environments and tree breeding for ornamental quality. These two genotypes showed a later bud burst phenology than the other U. minor clones, demonstrating suitability to areas with late frost events. The Spanish programme aims to substantially increase the range of tolerant native elms through new selections and crossings to gain a better understanding of the genetic basis of resistance.