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Let \(W\) be a Coxeter group and let \(\Phi^+\) be the positive roots. A subset \(B\) of \(\Phi^+\) is called "biclosed" if, whenever we have roots \(\alpha\), \(\beta\) and \(\gamma\) with \(\gamma \in \mathbb{R}_{›0} \alpha + \mathbb{R}_{›0} \beta\), if \(\alpha\) and \(\beta \in B\) then \(\gamma \in B\) and, if \(\alpha\) and \(\beta \not\in B\), then \(\gamma \not\in B\). The finite biclosed sets are the inversion sets of the elements of \(W\), and the containment between finite inversion sets is the weak order on \(W\). Dyer suggested studying the poset of all biclosed subsets of \(\Phi^+\), ordered by containment, and conjectured that it is a complete lattice. As progress towards Dyer's conjecture, we classify all biclosed sets in the affine root systems. We provide both a type uniform description, and concrete models in the classical types \(\widetilde{A}\), \(\widetilde{B}\), \(\widetilde{C}\), \(\widetilde{D}\). We use our models to prove that biclosed sets form a complete lattice in types \(\widetilde{A}\) and \(\widetilde{C}\), and we classify which biclosed sets are separable and which are weakly separable.Mathematics Subject Classifications: 20F55, 17B22, 06B23Keywords: Coxeter groups, root systems, affine Coxeter groups, lattice theory

One of the largest and longest standing societal challenges is acquiring enough food to support the human population. Our current era has the added complexities of the population nearing 9 billion, a globalized industrial agricultural production system, and a clearer understanding of how environmentally harmful and unsustainable that system is. While these issues are multifaceted, agriculture is fundamentally coupled with plant and microbial biology and there has been a diversity of avenues pursued by researchers seeking potential solutions and disruptive innovations to address our need to provide healthy food for the world without destroying it in the process. Modern agricultural practices currently require high energetic costs through extensive irrigation, application of synthetic fertilizers and pesticides, and the use of large, mechanized equipment. The lack of biodiversity in large-scale monoculture systems also presents issues in crop nutritional quality, disease pressure, and soil health. Recent advancements in our understanding of plant root systems and the relationships they form with soil microbiota have demonstrated a wealth of potential applications regarding these issues as well as in further illuminating the complex processes at play in plant health and development in an ecological context. It has become increasingly clear that plant roots are essential components to local and global nutrient cycling and drive much of the microbial activity in soils. In order to ensure a future with sustainable, climate-resilient agriculture which enables nutritious diets, we must continue to explore the wealth of knowledge underground. This dissertation seeks to clarify some of the socioeconomic reasons why we grow food the way we do and the limitations of material available for study, as well as underlying biochemical and genetic mechanisms which influence plant root biology and their relationships with microorganisms. The results of this research contribute to the g

In this article, we give a first example of a pair of quantum isomorphic, non-isomorphic strongly regular graphs, that is, non-isomorphic strongly regular graphs having the same homomorphism counts from all planar graphs. The pair consists of the orthogonality graph of the 120 lines spanned by the E8 root system and a rank 4 graph whose complement was first discovered by Brouwer, Ivanov and Klin. Both graphs are strongly regular with parameters (120, 63, 30, 36). Using Godsil-McKay switching, we obtain more quantum isomorphic, non-isomorphic strongly regular graphs with the same parameters.

In this article, we give a first example of a pair of quantum isomorphic, non-isomorphic strongly regular graphs, that is, non-isomorphic strongly regular graphs having the same homomorphism counts from all planar graphs. The pair consists of the orthogonality graph of the 120 lines spanned by the E8 root system and a rank 4 graph whose complement was first discovered by Brouwer, Ivanov and Klin. Both graphs are strongly regular with parameters (120, 63, 30, 36). Using Godsil-McKay switching, we obtain more quantum isomorphic, non-isomorphic strongly regular graphs with the same parameters.

©IOP Publishing. It is our pleasure to thank F. Calogero, A. Perelomov, and O. Ragnisco for useful discussions. D. G.-U. is also glad to acknowledge F. Calogero’s warm hospitality at Universitá di Roma (La Sapienza) while this work was in progress. This work is supported in part by DGES Grant PB98-0821., We develop a systematic procedure for constructing quantum many-body problems whose spectrum can be partially or totally computed by purely algebraic means. The exactly solvable models include rational and hyperbolic potentials related to root systems, in some cases with an additional external field. The quasi-exactly solvable models can be considered as deformations of the previous ones which share their algebraic character., DGES, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

Purpose Incorporating biosolids into the soil improves plant yield compared with surface application, but it can result in the increased uptake of trace elements. However, there is a lack of knowledge about how different types of biosolids applications affect soil quality. We aimed to determine the effect of the type and rate of biosolids application on soil quality and the mobility of contaminants. Methods Soil quality was determined by soil fertility (inorganic N, exchangeable P, Mg, Ca, K), exchangeable trace and non-essential elements (Al, Mn, Zn, Cu and Cd) and biological activity (dehydrogenase activity). We measured the properties of soil pore water, bulk soil and rhizosphere in a pot and a rhizobox experiment, with increasing concentration of biosolids (equiv. 16 t ha− 1, 48 t ha− 1 and 145 t ha− 1 dry weight), applied on the surface, incorporated to 25 cm, or incorporated into a patch. Results and discussion The incorporation of biosolids into the soil increased the exchangeable Zn, Cu, Cr, Ni and Cd, compared with surface application. The surface application of biosolids increased the inorganic N in the soil compared with biosolids incorporation (680 mg kg− 1 vs. 380 mg kg− 1), and decreased soil pH by 1.1 units. This aligned with solubilisation of Al (43 mg kg− 1 vs. 6 mg kg− 1) and Mn (43 mg kg− 1 vs. 33 mg kg− 1) and explains the decreased microbial activity in the soil compared with the unamended soil. Incorporating biosolids in the soil increased the biological activity, likely due to biosolids-borne microbes. The root systems significantly increased microbial activity, pH, and the concentration of NH4+, NO3−, and exchangeable P, S, Mg, Na, Zn, Cu and Ni, and significantly decreased exchangeable concentration of Mn and Fe.

The Root Systems in Sustainable Agricultural Intensification delivers a comprehensive treatment of state-of-the-art concepts in the theoretical and practical aspects of agricultural management to enhance root system architecture and function. The book emphasizes the agricultural measures that enhance root capacity to develop and function under a range of water and nutrient regimes to maximize food, feed, and fibre production, as well as minimize undesirable water and nutrient losses to the environment. This reference includes resources that discuss a variety of soil, plant, agronomy, farming system, breeding, molecular and modelling aspects to the subject. It also discusses strategies and mechanisms that underpin increased water- and nutrient-use efficiency and combines consideration of natural and agricultural systems to show the continuity of traits and mechanisms. Finally, the book explores issues related to the global economy as well as widespread social issues that arise from, or are underpinned by, agricultural intensification.

In previous joint work with J.-S. Koskivirta, we introduced the notion of quasi-constant character (of a maximal torus of a connected reductive group over a field); we showed that over an algebraically closed field it naturally unifies the notions minuscule and co-minuscule. In this note we characterize quasi-constant fundamental weights in terms of the Weyl group of the corresponding maximal Levi subgroup. Equivalently, purely in the language of root systems, the result characterizes special and co-special vertices of Dynkin diagrams in terms of the Weyl group of the corresponding maximal sub-root system.

Hoewel de positieve effecten van groen de nadelen ver overstijgen, zijn er wel degelijk momenten waarop het de nodige kopzorgen oplevert, met name in de stedelijke omgeving. Dat varieert van onkruidsoorten en invasieve exoten die groeien waar ze niet thuishoren, tot vegetatie die met haar houtige ledematen her en der het grijs van straten en gebouwen aantast. King RootBarrier belooft met zijn producten die hinder te omzeilen.

Hoewel de positieve effecten van groen de nadelen ver overstijgen, zijn er wel degelijk momenten waarop het de nodige kopzorgen oplevert, met name in de stedelijke omgeving. Dat varieert van onkruidsoorten en invasieve exoten die groeien waar ze niet thuishoren, tot vegetatie die met haar houtige ledematen her en der het grijs van straten en gebouwen aantast. King RootBarrier belooft met zijn producten die hinder te omzeilen.

We compute the total cohomology of the complement of the toric arrangement associated with the root system An as a representation of the corresponding Weyl group via fixed point theory of a twisted action of the group. We also provide several proofs of an explicit formula for the Poincare polynomial of the complement of the toric arrangement associated with An., Correction in: JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, Volume: 21, Issue: 4, Article Number: UNSP 89, DOI: 10.1007/s11784-019-0727-6

We compute the total cohomology of the complement of the toric arrangement associated with the root system An as a representation of the corresponding Weyl group via fixed point theory of a twisted action of the group. We also provide several proofs of an explicit formula for the Poincare polynomial of the complement of the toric arrangement associated with An., Correction in: JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, Volume: 21, Issue: 4, Article Number: UNSP 89, DOI: 10.1007/s11784-019-0727-6

We compute the total cohomology of the complement of the toric arrangement associated with the root system An as a representation of the corresponding Weyl group via fixed point theory of a twisted action of the group. We also provide several proofs of an explicit formula for the Poincare polynomial of the complement of the toric arrangement associated with An., Correction in: JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, Volume: 21, Issue: 4, Article Number: UNSP 89, DOI: 10.1007/s11784-019-0727-6

We compute the total cohomology of the complement of the toric arrangement associated with the root system An as a representation of the corresponding Weyl group via fixed point theory of a twisted action of the group. We also provide several proofs of an explicit formula for the Poincare polynomial of the complement of the toric arrangement associated with An., Correction in: JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, Volume: 21, Issue: 4, Article Number: UNSP 89, DOI: 10.1007/s11784-019-0727-6

We compute the total cohomology of the complement of the toric arrangement associated with the root system An as a representation of the corresponding Weyl group via fixed point theory of a twisted action of the group. We also provide several proofs of an explicit formula for the Poincare polynomial of the complement of the toric arrangement associated with An., Correction in: JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, Volume: 21, Issue: 4, Article Number: UNSP 89, DOI: 10.1007/s11784-019-0727-6

We compute the total cohomology of the complement of the toric arrangement associated with the root system An as a representation of the corresponding Weyl group via fixed point theory of a twisted action of the group. We also provide several proofs of an explicit formula for the Poincare polynomial of the complement of the toric arrangement associated with An., Correction in: JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, Volume: 21, Issue: 4, Article Number: UNSP 89, DOI: 10.1007/s11784-019-0727-6

We compute the total cohomology of the complement of the toric arrangement associated with the root system An as a representation of the corresponding Weyl group via fixed point theory of a twisted action of the group. We also provide several proofs of an explicit formula for the Poincare polynomial of the complement of the toric arrangement associated with An., Correction in: JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, Volume: 21, Issue: 4, Article Number: UNSP 89, DOI: 10.1007/s11784-019-0727-6

We compute the total cohomology of the complement of the toric arrangement associated with the root system An as a representation of the corresponding Weyl group via fixed point theory of a twisted action of the group. We also provide several proofs of an explicit formula for the Poincare polynomial of the complement of the toric arrangement associated with An., Correction in: JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, Volume: 21, Issue: 4, Article Number: UNSP 89, DOI: 10.1007/s11784-019-0727-6

We compute the total cohomology of the complement of the toric arrangement associated with the root system An as a representation of the corresponding Weyl group via fixed point theory of a twisted action of the group. We also provide several proofs of an explicit formula for the Poincare polynomial of the complement of the toric arrangement associated with An., Correction in: JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, Volume: 21, Issue: 4, Article Number: UNSP 89, DOI: 10.1007/s11784-019-0727-6

We compute the total cohomology of the complement of the toric arrangement associated with the root system An as a representation of the corresponding Weyl group via fixed point theory of a twisted action of the group. We also provide several proofs of an explicit formula for the Poincare polynomial of the complement of the toric arrangement associated with An., Correction in: JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, Volume: 21, Issue: 4, Article Number: UNSP 89, DOI: 10.1007/s11784-019-0727-6

We compute the total cohomology of the complement of the toric arrangement associated with the root system An as a representation of the corresponding Weyl group via fixed point theory of a twisted action of the group. We also provide several proofs of an explicit formula for the Poincare polynomial of the complement of the toric arrangement associated with An., Correction in: JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, Volume: 21, Issue: 4, Article Number: UNSP 89, DOI: 10.1007/s11784-019-0727-6

The accurate measurement of soil infiltration rates is a challenging task in hydrological studies, as they are governed by complex interactions between the plant and soil components. To explore the effects of plant roots and soil moisture (SM) on infiltration process, an automatic measurement system based on a point source device was used to determine infiltration rates at different cultivated grasslands (leguminous, gramineous and mixed) in an arid region of China. The results showed that SM and plant roots significantly affected the infiltration process at different stages in the three grasslands. The soil infiltration rates were negatively correlated to SM, but a positive correlation was observed with the below-ground biomass (BGB). SM was the main factor influencing the infiltration rates in the initial stage of infiltration, whereas both SM and BGB determined the steady-state infiltration rates. The influence of the combined effects of SM and plant roots decreased over infiltration time. The decreased rate of determining coefficient showed that SM was more influent than plant roots. These results may contribute to interpret the observed higher soil infiltration capacity in the leguminous grasslands than in the gramineous and the mixed grasslands, and were conducive to better understand the effects of plant and soil properties on infiltration processes in arid areas.

Root water uptake is critical for yield determination in agriculture. Water stress is indeed the most significant environmental stress in crops worldwide. It is even expected to become more and more severe in many regions of the globe while nowadays already millions of people remain chronically undernourished. In such context, understanding the plant mechanisms to efficiently take up water in a heterogeneous changing environment would be of great benefit in the quest for more resilient food production systems. Several authors proposed plant root system ideotypes for water uptake defined as ideal plant models, which are expected to yield a greater quantity or quality of grain when developed as cultivars. Such plant models are characterized by an ensemble of properties (alternatively called phene states) that are responsible for their improved performance in terms of transpiration, such as root structural (e.g. root length, elongation rates) and functional (e.g. radial or axial hydraulic conductivity) properties. However current definitions of crop root system ideotypes are of limited in terms of interest for several reasons. They usually do not contain quantitative characteristics and do not include the time dimension. They are not associated to specific pedo-climatic conditions while it has been demonstrated that no root system can perform ideally in any situation. Furthermore root water uptake strategy is not uniquely defined by an ensemble of phene states: other combinations of phene states could lead to similar water uptake behaviors. The main objective of this thesis is to advance the current understanding of plant optimal water uptake and growth strategies for maximising crop yield. Such plants would minimize the water stress over their crop cycle and particularly at critical development stages. New definitions of crop quantitative eco-ideotypes for root water uptake, i.e. ideal root systems that avoid water stress over their crop cycle or, at least, at floweri, (AGRO - Sciences agronomiques et ingénierie biologique) -- UCL, 2017

Within the project ‘Plant champion air purification’, a public-private cooperation, a literate survey was carried out to explore recent findings on the possibilities of plants to purify indoor contaminated air. Literature was searched in academic journals, on the internet and within reports recently carried out for the horticultural sector. Here this knowledge is shortly described. Plants generally have the capacity to assimilate hydrophilic Volatile Organic Compounds (VOCs) like formaldehyde without harm. Lipophilic VOCs are less well assimilated and follow different uptake pathways. Differences between plant species can sometimes be related to amount of leaves, wax layer composition, stomatal conductance or hairs. Apart from the green plant parts, the roots, the micro-organisms and rooting medium have a role in air purification. The research in plant chambers mainly generated knowledge on short term uptake of volatiles, but the uptake mechanisms and the long-term performances of plants are only partly understood. The research on upscaling of lab results to air purification in rooms within buildings is still in its infancy. A few good studies have been done and show promising results, but most research was statistically poor. More research is needed to extrapolate the findings from lab research to practice., Binnen het project ‘Plantkampioen luchtzuivering’, een publiek-private samenwerking, is een literatuurstudie uitgevoerd naar de meest recente bevindingen over de mogelijkheid van planten om lucht binnenshuis te zuiveren. Er is gezocht in wetenschappelijke publicaties, vakbladen en tuinbouwrapporten. Het algemene beeld is dat planten in zekere mate Vluchtige Organische Stof (VOS) kunnen opnemen zonder zelf schade te ondervinden. De opnamemechanismen verschillen tussen typen VOS. Hydrofiele VOS zoals formaldehyde worden vrij goed door het blad verwerkt, terwijl lipofiele componenten via andere routes worden opgenomen. Verschillen tussen plantensoorten houden verband met de hoeveelheid blad, de huidmondjesopening, de waslaag en de beharing. Naast de groene plantendelen spelen ook de wortels, de micro-organismen en het substraat een rol in de luchtzuivering. Het onderzoek in plantkamers leverde vooral resultaten over de kortdurende opnamen door planten, maar over de lange-termijn effecten en de onderliggende mechanismen is nog weinig bekend. Het onderzoek naar opschaling van lab- naar praktijksituaties is nog weinig ontwikkeld. Enkele goede studies laten veelbelovende resultaten zien, maar veel onderzoek is matig onderbouwd. Meer onderzoek is nodig om de labproeven te kunnen extrapoleren naar de praktijk.

In this article, we investigate the existence of joins in the weak order of an infinite Coxeter group W. We give a geometric characterization of the existence of a join for a subset X in W in terms of the inversion sets of its elements and their position relative to the imaginary cone. Finally, we discuss inversion sets of infinite reduced words and the notions of biconvex and biclosed sets of positive roots.

Agrariërs zijn op velerlei manieren bezig met de hydrologische toestand van hun percelen en het weer en hoe hierop in te spelen door beregening en drainage. Binnen de Topsector Water proberen onderzoekers nauwkeuriger de hoeveelheid bodemvocht in de wortelzone te voorspellen. Dit is belangrijk voor de groei van landbouwgewassen.

De meeste mensen weten niet goed hoe bomen en de bodem in elkaar zitten en hoe uitgebreid het wortelgestel is.

In his affirmative answer to the Edelman-Reiner conjecture, Yoshinaga proved that the logarithmic derivation modules of the cones of the extended Shi arrangements are free modules. However, we know very little about the bases themselves except their existence. In this article, we prove the unique existence of two distinguished bases which we call the simple-root basis plus (SRB+) and the simple-root basis minus (SRB-). They are characterized by nice divisibility properties relative to the simple roots.

The aim of this paper is to introduce the methods by which we can examine and evaluate the root system of the tree individuals. Methods rank among method of the Contact flora assessment "CFA", especially subsystem C: functional diagnostics. "CFA" is one of the subsystems Forensic ecotechnique: forest and trees., Cílem tohoto příspěvku je seznámit s metodami, kterými můžeme zkoumat a ohodnocovat kořenový systém stromových jedinců. Metody řadíme mezi metody Kontaktního ohodnocování rostlinstva "CFA", zejména subsystém C: funkční diagnostika. "CFA" je jeden ze subsystémů oboru Forenzní ekotechnika: les a dřeviny.

In his affirmative answer to the Edelman-Reiner conjecture, Yoshinaga proved that the logarithmic derivation modules of the cones of the extended Shi arrangements are free modules. However, we know very little about the bases themselves except their existence. In this article, we prove the unique existence of two distinguished bases which we call the simple-root basis plus (SRB+) and the simple-root basis minus (SRB-). They are characterized by nice divisibility properties relative to the simple roots.

Nieuwe persoonlijk hoogleraar Plantenecologie. Hoe meer soorten, hoe minder schimmels.

• Nieuwe persoonlijk hoogleraar Plantenecologie. • Hoe meer soorten, hoe minder schimmels.

Pius Floris van Plant Health Cure schrijft in iedere editie van KAS een artikel waarmee hij telers wil aansporen om anders tegen bemesting en biologie in de kas aan te kijken. Hij doet dat als internationaal erkend deskundige op het gebied van kennis over een gezonde omgeving rondom de wortels van een plant, of dat nu in de grond is of in een substraat. In dit artikel wordt vooral ingegaan op het transportsysteem in planten.

The moduli space of curves endowed with a nonzero abelian differential admits a natural stratification according to the configuration of its zeroes. We give a description of these strata for genus 3 in terms of root system data. For each non-open stratum we obtain a presentation of its orbifold fundamental group.

The aim of this paper is to introduce the methods by which we can examine and evaluate the root system of the tree individuals. Methods rank among method of the Contact flora assessment "CFA", especially subsystem C: functional diagnostics. "CFA" is one of the subsystems Forensic ecotechnique: forest and trees., Cílem tohoto příspěvku je seznámit s metodami, kterými můžeme zkoumat a ohodnocovat kořenový systém stromových jedinců. Metody řadíme mezi metody Kontaktního ohodnocování rostlinstva "CFA", zejména subsystém C: funkční diagnostika. "CFA" je jeden ze subsystémů oboru Forenzní ekotechnika: les a dřeviny.

The aim of this paper is to introduce the methods by which we can examine and evaluate the root system of the tree individuals. Methods rank among method of the Contact flora assessment "CFA", especially subsystem C: functional diagnostics. "CFA" is one of the subsystems Forensic ecotechnique: forest and trees., Cílem tohoto příspěvku je seznámit s metodami, kterými můžeme zkoumat a ohodnocovat kořenový systém stromových jedinců. Metody řadíme mezi metody Kontaktního ohodnocování rostlinstva "CFA", zejména subsystém C: funkční diagnostika. "CFA" je jeden ze subsystémů oboru Forenzní ekotechnika: les a dřeviny.

The aim of this paper is to introduce the methods by which we can examine and evaluate the root system of the tree individuals. Methods rank among method of the Contact flora assessment "CFA", especially subsystem C: functional diagnostics. "CFA" is one of the subsystems Forensic ecotechnique: forest and trees., Cílem tohoto příspěvku je seznámit s metodami, kterými můžeme zkoumat a ohodnocovat kořenový systém stromových jedinců. Metody řadíme mezi metody Kontaktního ohodnocování rostlinstva "CFA", zejména subsystém C: funkční diagnostika. "CFA" je jeden ze subsystémů oboru Forenzní ekotechnika: les a dřeviny.

The aim of this paper is to introduce the methods by which we can examine and evaluate the root system of the tree individuals. Methods rank among method of the Contact flora assessment "CFA", especially subsystem C: functional diagnostics. "CFA" is one of the subsystems Forensic ecotechnique: forest and trees., Cílem tohoto příspěvku je seznámit s metodami, kterými můžeme zkoumat a ohodnocovat kořenový systém stromových jedinců. Metody řadíme mezi metody Kontaktního ohodnocování rostlinstva "CFA", zejména subsystém C: funkční diagnostika. "CFA" je jeden ze subsystémů oboru Forenzní ekotechnika: les a dřeviny.

The aim of this paper is to introduce the methods by which we can examine and evaluate the root system of the tree individuals. Methods rank among method of the Contact flora assessment "CFA", especially subsystem C: functional diagnostics. "CFA" is one of the subsystems Forensic ecotechnique: forest and trees., Cílem tohoto příspěvku je seznámit s metodami, kterými můžeme zkoumat a ohodnocovat kořenový systém stromových jedinců. Metody řadíme mezi metody Kontaktního ohodnocování rostlinstva "CFA", zejména subsystém C: funkční diagnostika. "CFA" je jeden ze subsystémů oboru Forenzní ekotechnika: les a dřeviny.

The aim of this paper is to introduce the methods by which we can examine and evaluate the root system of the tree individuals. Methods rank among method of the Contact flora assessment "CFA", especially subsystem C: functional diagnostics. "CFA" is one of the subsystems Forensic ecotechnique: forest and trees., Cílem tohoto příspěvku je seznámit s metodami, kterými můžeme zkoumat a ohodnocovat kořenový systém stromových jedinců. Metody řadíme mezi metody Kontaktního ohodnocování rostlinstva "CFA", zejména subsystém C: funkční diagnostika. "CFA" je jeden ze subsystémů oboru Forenzní ekotechnika: les a dřeviny.

The aim of this paper is to introduce the methods by which we can examine and evaluate the root system of the tree individuals. Methods rank among method of the Contact flora assessment "CFA", especially subsystem C: functional diagnostics. "CFA" is one of the subsystems Forensic ecotechnique: forest and trees., Cílem tohoto příspěvku je seznámit s metodami, kterými můžeme zkoumat a ohodnocovat kořenový systém stromových jedinců. Metody řadíme mezi metody Kontaktního ohodnocování rostlinstva "CFA", zejména subsystém C: funkční diagnostika. "CFA" je jeden ze subsystémů oboru Forenzní ekotechnika: les a dřeviny.

We overcome the barrier of constructing N - 4 superconformal models in one space dimension for more than three particles. The D(2, 1; alpha) superalgebra of our systems is realized on the coordinates and momenta of the particles, their superpartners and one complex pair of harmonic variables. The models are determined by two prepotentials, F and U, which must obey the WDVV and a Killing-type equation plus homogeneity conditions. We investigate permutation-symmetric solutions, with and without translation invariance. Models based on deformed An and BCDn root systems are constructed for any value of alpha, and exceptional F-n-type and super root systems admit solutions as well. Translation-invariant mechanics occurs for any number of particles at alpha=-1/2 (osp(4/2) invariance as a degenerate limit) and for four particles at arbitrary alpha (three series).