On the Nielsen root theory of n-valued maps

Let $$\phi :X \multimap Y$$ ϕ : X ⊸ Y be an n-valued map of connected finite polyhedra and let $$a \in Y$$ a ∈ Y . Then, $$x \in X$$ x ∈ X is a root of $$\phi $$ ϕ at a if $$a \in \phi (x)$$ a ∈ ϕ ( x ) . The Nielsen root number $$N(\phi : a)$$ N ( ϕ : a ) is a lower bound for the number of roots at a of any n-valued map homotopic to $$\phi $$ ϕ . We prove that if X and Y are compact, connected triangulated manifolds without boundary, of the same dimension, then given $$\epsilon > 0$$ ϵ > 0 , there is an n-valued map $$\psi $$ ψ homotopic to $$\phi $$ ϕ within Hausdorff distance $$\epsilon $$ ϵ of $$\phi $$ ϕ such that $$\psi $$ ψ has finitely many roots at a. We conjecture that if X and Y are q-manifolds without boundary, $$q \ne 2$$ q ≠ 2 , then there is an n-valued map homotopic to $$\phi $$ ϕ that has $$N(\phi : a)$$ N ( ϕ : a ) roots at a. We verify the conjecture when $$X = Y$$ X = Y is a Lie group by employing a fixed point result of Schirmer. As an application, we calculate the Nielsen root numbers of linear n-valued maps of tori.

Contrasting ability of deep and shallow rooting rice genotypes to grow through plough pans containing simulated biopores and cracks

Aims Cracks and biopores in compacted soil such as plough pans could aid deep rooting, mitigating constraints to seasonal upland use of paddy fields for rice production. This research investigated how soil macropores through a simulated plough pan affects root growth of contrasting deep and shallow rooting rice genotypes. Methods Deep rooting Black Gora and shallow rooting IR64 rice varieties were grown in packed cores of unsaturated soil in a controlled greenhouse. Simulated biopores and cracks (macropores) were inserted through the plough pan to form treatments with no macropores, biopores, cracks, and combined cracks and biopores. Different root parameters such as root length density (RLD), root volume, root diameter, number of root tips and branches were measured. The number of roots was calculated manually, including the number of roots growing through macropores in the plough pan layer. Results Plough pans with macropores had 25–32% more roots than with no macropores. RLD was 55% greater in the plough pan layer if cracks were present compared to biopores. Conversely, RLD was 26% less in subsoil if the plough pan had cracks compared to biopores. Different root parameters were greatly influenced by the presence of macropores in the plough pan, and deep-rooted Black Gora produced 81% greater RLD, 30% more root numbers and 103% more branching than the shallow rooted rice genotype IR64 within the plough pan layer. Conclusions Macropores greatly improve rice root growth through plough pans for a deep rooting but not a shallow rooting rice variety. Whereas cracks produce a greater number of roots in the plough pan, biopores result in greater root branching and root numbers deeper in subsoil.

SmSPL6 Induces Phenolic Acid Biosynthesis and Affects Root Development in Salvia miltiorrhiza

Salvia miltiorrhiza is a renowned model medicinal plant species for which 15 SQUAMOSA PROMOTER BINDING PROTEIN-LIKE (SPL) family genes have been identified; however, the specific functions of SmSPLs have not been well characterized as of yet. For this study, the expression patterns of SmSPL6 were determined through its responses to treatments of exogenous hormones, including indole acetic acid (IAA), gibberellic acid (GA3), methyl jasmonic acid (MeJA), and abscisic acid (ABA). To characterize its functionality, we obtained SmSPL6-ovexpressed transgenic S. miltiorrhiza plants and found that overexpressed SmSPL6 promoted the accumulation of phenolic acids and repressed the biosynthesis of anthocyanin. Meanwhile, the root lengths of the SmSPL6-overexpressed lines were significantly longer than the control; however, both the fresh weights and lateral root numbers decreased. Further investigations indicated that SmSPL6 regulated the biosynthesis of phenolic acid by directly binding to the promoter regions of the enzyme genes Sm4CL9 and SmCYP98A14 and activated their expression. We concluded that SmSPL6 regulates not only the biosynthesis of phenolic acids, but also the development of roots in S. miltiorrhiza.

SUBSTRATES AND INDOLE-3-BUTYRIC ACID IN MINI-CUTTINGS ROOTING OF Carya illinoinensis (WANGENH) K. KOCH

Mini-cutting technique of tree species is an effective method of maintaining desirable features of plant matrices and uniformity. The objective of the present research was to determine substrate and concentration of indolebutyric acid (IBA) more suitable for mini-cuttings of Carya illinoinensis rooting. The experiment was carried out in a greenhouse with mist, from February to May 2018. The used experimental design was in blocks with a factorial arrangement of 3 x 5, in which three substrates were tested: carbonized rice husk, vermiculite and perlit; and five IBA concentration : 0, 2,000, 4,000, 6,000 and 8,000 mg L-1. The mini-cuttings were apical, produced from seedlings, with eight months of age. Mini-cuttings were made with two leaves cut in half and 8 to 10 cm in length. The use of IBA influenced results obtained with all substrates, except for the variable number of roots, in which only IBA effect was observed. However, higher results were obtained with IBA uses together with substrate carbonized rice husk, obtaining estimated maximum point of 91% of rooted mini-cuttings with 3,957 mg L-1 IBA concentration. For other evaluated variables, except root numbers, it was also observed superior results close to 4,000 mg L-1 IBA concentration with substrate carbonized rice husk. Results indicate the possibility of Carya illinoinensis propagation by mini-cutting technique and as an alternative for this specie plantlets production.

Contrasting Ability of Deep and Shallow Rooting Rice Genotypes to Grow Through Plough Pans Containing Biopores and Cracks

Aims Cracks and biopores in compacted soil such as plough pans could aid deep rooting, mitigating constraints to seasonal upland use of paddy fields for rice production. This research investigated how soil macropores through a simulated plough pan affects root growth of contrasting deep and shallow rooting rice genotypes.Methods Deep rooting Black Gora and shallow rooting IR64 rice varieties were grown in packed cores of unsaturated soil in a controlled greenhouse. Artificial biopores and cracks (macropores) were inserted through the plough pan to form treatments with no macropores, biopores, cracks, and combined cracks and biopores. Different root parameters such as root length density (RLD), root volume, root diameter, number of root tips and branches were measured. The number of roots was calculated manually, including the number of roots growing through macropores in the plough pan layer.Results Plough pans with macropores had 25-32 % more roots than with no macropores. RLD was 55 % greater in the plough pan layer if cracks were present compared to biopores. Conversely, RLD was 26 % less in subsoil if the plough pan had cracks compared to biopores. Different root parameters were greatly influenced by the presence of macropores in the plough pan, and deep-rooted Black Gora produced 81% greater RLD, 30 % more root numbers and 103 % more branching than the shallow rooted rice genotype IR64 within the plough pan layer.Conclusions Macropores greatly improve rice root growth through plough pans for a deep rooting but not shallow rooting rice variety. Whereas cracks produce a greater number of roots in the plough pan, biopores result in greater root branching and root numbers deeper in subsoil.

Distribution of root numbers of Hecke characters attached to some elliptic curves

In this paper, we show that an action on the set of elliptic curves with j = 1728 j=1728 preserves a certain kind of symmetry on the local root number of Hecke characters attached to such elliptic curves. As a consequence, we give results on the distribution of the root numbers and their average of the aforementioned Hecke characters.

Production systems and methods affect the quality and the quantity of saffron (Crocus sativus L.)

Aim of study: Comparison of saffron flowering between open field and controlled environment. Possibility of saffron transplanting.Area of study: University of Birjand (Iran)Material and methods: In a first experiment, saffron yield and quality produced by traditional production system (TPS) and by soilless one (SPS) were compared. In a second experiment, the effects of the production method, by direct planting (DP) or by transplanting plant (TP) in open field were studied.Main results: Percentage of flowering corms grown by SPS was 39% and 65%, while by TPS was 6% and 56% in 2018 and 2019, respectively. Flower and stigma yields were significantly higher by SPS than by TPS. Stigma obtained from SPS had higher L (lightness) and crocin. Safranal content was higher in stigma produced by TPS. Leaf and root numbers and corm weight were higher for SPS, but after transplanting there was better status for DP than for TP. At the end of the first growing season (2018-19), mean replacement corms weight (4.4 vs 3.0 g), replacement corms yield (21.3 vs 12.8 g per plant), weight of main replacement corm (11.7 vs 6.0 g) and number of large replacement corms (0.6 vs 0.1 corms per plant) for DP were significantly higher than for TP. However, during the second growing season (2019-20), the plants in TP plots improved their performances.Research highlights: Saffron production was more favorable under controlled environment. Transplanting is possible, but there is a need to improve methods to gain more favorable results.