Coverage and invariance for the biological control of pests in mediterranean greenhouses

A major problem related to the treatment of ecosystems is that they have no available mathematical formalization. This implies that many of their properties are not presented as short, rigorous modalities, but rather as long expressions which, from a biological standpoint, totally capture the significance of the property, but which have the disadvantage of not being sufficiently manageable, from a mathematical standpoint. The interpretation of ecosystems through networks allows us to employ the concepts of coverage and invariance alongside other related concepts. The latter will allow us to present the two most important relations in an ecosystem – predator–prey and competition – in a different way. Biological control, defined as “the use of living organisms, their resources or their products to prevent or reduce loss or damage caused by pests”, is now considered the environmentally safest and most economically advantageous method of pest control (van Lenteren, 2011). A guild includes all those organisms that share a common food resource (Polis et al., 1989), which in the context of biological control means all the natural enemies of a given pest. There are several types of intraguild interactions, but the one that has received most research attention is intraguild predation, which occurs when two organisms share the same prey while at the same time participating in some kind of trophic interaction. However, this is not the only intraguild relationship possible, and studies are now being conducted on others, such as oviposition deterrence. In this article, we apply the developed concepts of structural functions, coverage, invariant sets, etc. (Lloret et al., 1998, Esteve and Lloret, 2006a, Esteve and Lloret, 2006b and Esteve and Lloret, 2007) to a tritrophic system that includes aphids, one of the most damaging pests and a current bottleneck for the success of biological control in Mediterranean greenhouses.

School Anxiety Inventory–Short Version: Factorial Invariance and Latent Mean Differences Across Gender and Age in Spanish Adolescents

This study examined the factorial invariance and latent mean differences of the School Anxiety Inventory–Short Version across gender and age groups for 2,367 Spanish students, ranging in age from 12 to 18 years. Configural and measurement invariance were found across gender and age samples for all dimensions of the School Anxiety Inventory–Short Version.

On the Result of Invariance of the Closure Set of the Real Projections of the Zeros of an Important Class of Exponential Polynomials

In this paper we provide the proof of a practical point-wise characterization of the set RP defined by the closure set of the real projections of the zeros of an exponential polynomial P(z) = Σn j=1 cjewjz with real frequencies wj linearly independent over the rationals. As a consequence, we give a complete description of the set RP and prove its invariance with respect to the moduli of the c′ js, which allows us to determine exactly the gaps of RP and the extremes of the critical interval of P(z) by solving inequations with positive real numbers. Finally, we analyse the converse of this result of invariance.