On the Moore Formula of Compact Nilmanifolds

Let G be a connected and simply connected two-step nilpotent Lie group and Γ a lattice subgroup of G. In this note, we give a new multiplicity formula, according to the sense of Moore, of irreducible unitary representations involved in the decomposition of the quasi-regular representation IndΓG(1). Extending then the Abelian case

Discrete Cocompact Subgroups of the Five-Dimensional Connected and Simply Connected Nilpotent Lie Groups

The discrete cocompact subgroups of the five-dimensional connected, simply connected nilpotent Lie groups are determined up to isomorphism. Moreover, we prove if G = N × A is a connected, simply connected, nilpotent Lie group with an Abelian factor A, then every uniform subgroup of G is the direct product of a uniform subgroup of N and Zr where r = dim A

Utjecaj uvjeta uzgoja i dodatka soli na sastav eteričnog ulja slatkog mažurana (Origanum majorana) iz Tunisa

O. majorana shoots were investigated for their essential oil (EO) composition. Two experiments were carried out; the first on hydroponic medium in a culture chamber and the second on inert sand in a greenhouse for 20 days. Plants were cultivated for 17 days in hydroponic medium supplemented with NaCl 100 mmol L1. The results showed that the O. majorana hydroponic medium offered higher essential oil yield than that from the greenhouse. The latter increased significantly in yield (by 50 %) under saline constraint while it did not change in the culture chamber. Under greenhouse conditions and in the absence of salt treatment, the major constituents were terpinene-4-ol and trans-sabinene hydrate. However, in the culture chamber, the major volatile components were cis-sabinene hydrate and terpinene-4-ol. In the presence of NaCl, new compounds appeared, such as eicosane, spathulenol, eugenol, and phenol. In addition, in the greenhouse, with or without salt, a very important change of trans-sabinene hydrate concentration in EO occurred, whereas in the culture chamber change appeared in cis-sabinene hydrate content.U radu je opisano ispitivanje sastava eteričnog ulja izdanaka biljke O. majorana. Provedena su dva eksperimenta: prvi na hidroponom mediju u komorama za uzgoj, a drugi na inertnom pijesku u stakleniku tijekom 20 dana. Biljke su uzgajane 17 dana u hidroponom mediju u koji je dodan NaCl 100 mmol L1. Rezultati ukazuju na to da hidroponi medij O. majorana osigurava veće prinose eteričnog ulja nego staklenik. U stakleniku se prinos ulja značajno povećao dodavanjem 50 % soli dok u uzgoju u uzgojnoj komori nije bilo promjene. U uvjetima u stakleniku i u odsutnosti soli, najvažniji sastojci ulja bili su terpinen-4-ol i trans-sabinen hidrat, dok su u uvjetima uzgojne komore najvažnije hlapljive komponente bile cis-sabinen hidrat i terpinen-4-ol. U prisutnosti NaCl-a, pojavili su se novi sastojci, kao što su eikozan, spatulenol, eugenol i fenol. Dodatno je uz stakleničke uvjete, sa i bez soli, došlo do važne promjene u količini trans-sabinen hidrata u eteričnom ulju, dok se u komorama promijenio sadržaj cis-sabinen hidrata

Grapevine rootstocks shape underground bacterial microbiome and networking but not potential functionality

BackgroundThe plant compartments of Vitis vinifera, including the rhizosphere, rhizoplane, root endosphere, phyllosphere and carposphere, provide unique niches that drive specific bacterial microbiome associations. The majority of phyllosphere endophytes originate from the soil and migrate up to the aerial compartments through the root endosphere. Thus, the soil and root endosphere partially define the aerial endosphere in the leaves and berries, contributing to the terroir of the fruit. However, V. vinifera cultivars are invariably grafted onto the rootstocks of other Vitis species and hybrids. It has been hypothesized that the plant species determines the microbiome of the root endosphere and, as a consequence, the aerial endosphere. In this work, we test the first part of this hypothesis. We investigate whether different rootstocks influence the bacteria selected from the surrounding soil, affecting the bacterial diversity and potential functionality of the rhizosphere and root endosphere.MethodsBacterial microbiomes from both the root tissues and the rhizosphere of Barbera cultivars, both ungrafted and grafted on four different rootstocks, cultivated in the same soil from the same vineyard, were characterized by 16S rRNA high-throughput sequencing. To assess the influence of the root genotype on the bacterial communities’ recruitment in the root system, (i) the phylogenetic diversity coupled with the predicted functional profiles and (ii) the co-occurrence bacterial networks were determined. Cultivation-dependent approaches were used to reveal the plant-growth promoting (PGP) potential associated with the grafted and ungrafted root systems.ResultsRichness, diversity and bacterial community networking in the root compartments were significantly influenced by the rootstocks. Complementary to a shared bacterial microbiome, different subsets of soil bacteria, including those endowed with PGP traits, were selected by the root system compartments of different rootstocks. The interaction between the root compartments and the rootstock exerted a unique selective pressure that enhanced niche differentiation, but rootstock-specific bacterial communities were still recruited with conserved PGP traits.ConclusionWhile the rootstock significantly influences the taxonomy, structure and network properties of the bacterial community in grapevine roots, a homeostatic effect on the distribution of the predicted and potential functional PGP traits was found

TRACE ELEMENTS LATERAL DISTRIBUTION AND LIMITATIONS FOR REVEGETATION IN LEAD MINE SOILS: CASE OF LAKHOUAT MINE, TUNISIA

<p>Anthropogenic activities such as mining have increased the prevalence and occurrence of trace elements soil contamination. Abandoned mine tailings cause the contamination of adjacent agricultural soils. In Lakhouat mining area (West-Northern Tunisia), the dispersion of particles containing Pb, Zn and Cd results in the contamination of the surrounding agricultural soils. These soils presented high concentrations of Pb (1272 mg kg^-1), Zn (5543 mg kg^-1) and Cd (25 mg kg^-1). Furthermore, the tailing sample and soil sample close the dam tailing presented higher concentrations of Pb, Zn and Cd and conferred more limitation factors for revegetation than adjacent soils of mining area. The main limiting factors of mine soils are their low effective depth, low organic matter content and low phosphorus content and an imbalance between potassium and manganese exchangeable cations. These mine soils are strongly affected by high Pb, Zn and Cd levels which hinder revegetation.</p