Optimal quality of exceptional points for the Lebesgue density theorem

In spite of the Lebesgue density theorem, there is a positive $\delta$ such that, for every non-trivial measurable set $S$ of real numbers, there is a point at which both the lower densities of $S$ and of the complement of $S$ are at least $\delta$. The problem of determining the supremum of possible values of this $\delta$ was studied in a paper of V. I. Kolyada, as well as in some recent papers. We solve this problem in the present work.Comment: 45 page

On the 3D steady flow of a second grade fluid past an obstacle

We study steady flow of a second grade fluid past an obstacle in three space dimensions. We prove existence of solution in weighted Lebesgue spaces with anisotropic weights and thus existence of the wake region behind the obstacle. We use properties of the fundamental Oseen tensor together with results achieved in \cite{Koch} and properties of solutions to steady transport equation to get up to arbitrarily small \ep the same decay as the Oseen fundamental solution

An ectomycorrhizal fungus alters sensitivity to jasmonate, salicylate, gibberellin, and ethylene in host roots.

The phytohormones jasmonate, gibberellin, salicylate, and ethylene regulate an interconnected reprogramming network integrating root development with plant responses against microbes. The establishment of mutualistic ectomycorrhizal symbiosis requires the suppression of plant defense responses against fungi as well as the modification of root architecture and cortical cell wall properties. Here, we investigated the contribution of phytohormones and their crosstalk to the ontogenesis of ectomycorrhizae (ECM) between grey poplar (Populus tremula x alba) roots and the fungus Laccaria bicolor. To obtain the hormonal blueprint of developing ECM, we quantified the concentrations of jasmonates, gibberellins, and salicylate via liquid chromatography-tandem mass spectrometry. Subsequently, we assessed root architecture, mycorrhizal morphology, and gene expression levels (RNA sequencing) in phytohormone-treated poplar lateral roots in the presence or absence of L. bicolor. Salicylic acid accumulated in mid-stage ECM. Exogenous phytohormone treatment affected the fungal colonization rate and/or frequency of Hartig net formation. Colonized lateral roots displayed diminished responsiveness to jasmonate but regulated some genes, implicated in defense and cell wall remodelling, that were specifically differentially expressed after jasmonate treatment. Responses to salicylate, gibberellin, and ethylene were enhanced in ECM. The dynamics of phytohormone accumulation and response suggest that jasmonate, gibberellin, salicylate, and ethylene signalling play multifaceted roles in poplar L. bicolor ectomycorrhizal development

Unambiguous coherent state identification: Searching a quantum database

We consider an unambiguous identification of an unknown coherent state with one of two unknown coherent reference states. Specifically, we consider two modes of an electromagnetic field prepared in unknown coherent states alpha_1 and alpha_2, respectively. The third mode is prepared either in the state alpha_1 or in the state alpha_2. The task is to identify (unambiguously) which of the two modes are in the same state. We present a scheme consisting of three beamsplitters capable to perform this task. Although we don't prove the optimality, we show that the performance of the proposed setup is better than the generalization of the optimal measurement known for a finite-dimensional case. We show that a single beamsplitter is capable to perform an unambiguous quantum state comparison for coherent states optimally. Finally we propose an experimental setup consisting of 2N-1 beamsplitters for unambiguous identification among N unknown coherent states. This setup can be considered as a search in a quantum database. The elements of the database are unknown coherent states encoded in different modes of an electromagnetic field. The task is to specify the two modes that are excited in the same, though unknown, coherent state.Comment: version accepted for publication, 12 pages, 3 figure

Investigation of biomass and agricultural plastic co-pyrolysis: Effect on biochar yield and properties

Complete separation of mixed plastic and biomass waste is a technically difficult, laborious, expensive and time-consuming process. Hence, co-pyrolysis of these agricultural waste streams with low levels of plastic contamination presents a novel approach for the management of these plastic containing wastes, producing stable forms of carbon with potential use in environmental, agricultural and industrial applications. In this study, spent growing medium along with plastic growing bags, and bean crop residues along with mulching sheets were selected to assess how the presence of plastics would affect the characteristics of the biochars produced. These feedstocks were combined in mass ratios (of plastic in the biomass-plastic mixture) of 0, 0.25, 2.5, 5 and 10%. The resulting feedstock underwent slow pyrolysis in a fixed bed pyrolysis reactor at a temperature of 550 °C to ensure complete conversion of the plastic components of the feedstock. From the results obtained from pyrolysis, low ratios of plastic were found to have a positive impact on biochar yield, while high plastic ratios were found to have negative effect. Higher level of plastic in the feedstock have resulted peculiar functional groups in the biochar, including carboxylate anions, amides and aromatic groups. Biochars produced from spent growing medium along with plastic grow bags (GM biochars) showed no phytotoxic effect, irrespective of the concentration of plastic contamination in the feedstock. Biochars produced from bean crop residues along with mulching sheets (BM biochars) on the other hand showed high level of phytotoxicity (zero germination), irrespective of level of plastic contamination. After washing all BM biochar, very low phytotoxicity levels with no statistically significant effect of plastic contamination were observed, with the exception of 10BM that showed somewhat a reduced germination rate (93%). The results of this study will be beneficial for determining the tolerable level of plastic contamination in managing mixed agricultural waste biomass and to produce biochars suitable for environmental, agricultural and/or industrial applications

Odderon Exchange from Elastic Scattering Differences between pp and p¯p Data at 1.96 TeV and from pp Forward Scattering Measurements

We describe an analysis comparing the p¯p elastic cross section as measured by the D0 Collaboration at a center-of-mass energy of 1.96 TeV to that in pp collisions as measured by the TOTEM Collaboration at 2.76, 7, 8, and 13 TeV using a model-independent approach. The TOTEM cross sections, extrapolated to a center-of-mass energy of √s=1.96 TeV, are compared with the D0 measurement in the region of the diffractive minimum and the second maximum of the pp cross section. The two data sets disagree at the 3.4σ level and thus provide evidence for the t-channel exchange of a colorless, C-odd gluonic compound, also known as the odderon. We combine these results with a TOTEM analysis of the same C-odd exchange based on the total cross section and the ratio of the real to imaginary parts of the forward elastic strong interaction scattering amplitude in pp scattering for which the significance is between 3.4σ and 4.6σ. The combined significance is larger than 5σ and is interpreted as the first observation of the exchange of a colorless, C-odd gluonic compound