Uniqueness of radial solutions for the fractional Laplacian

We prove general uniqueness results for radial solutions of linear and nonlinear equations involving the fractional Laplacian $(-\Delta)^s$ with $s \in (0,1)$ for any space dimensions $N \geq 1$. By extending a monotonicity formula found by Cabre and Sire \cite{CaSi-10}, we show that the linear equation $(-\Delta)^s u+ Vu = 0$ in $\mathbb{R}^N$ has at most one radial and bounded solution vanishing at infinity, provided that the potential $V$ is a radial and non-decreasing. In particular, this result implies that all radial eigenvalues of the corresponding fractional Schr\"odinger operator $H=(-\Delta)^s + V$ are simple. Furthermore, by combining these findings on linear equations with topological bounds for a related problem on the upper half-space $\mathbb{R}^{N+1}_+$, we show uniqueness and nondegeneracy of ground state solutions for the nonlinear equation $(-\Delta)^s Q + Q - |Q|^{\alpha} Q = 0$ in $\mathbb{R}^N$ for arbitrary space dimensions $N \geq 1$ and all admissible exponents $\alpha >0$. This generalizes the nondegeneracy and uniqueness result for dimension N=1 recently obtained by the first two authors in \cite{FrLe-10} and, in particular, the uniqueness result for solitary waves of the Benjamin--Ono equation found by Amick and Toland \cite{AmTo-91}.Comment: 38 pages; revised version; various typos corrected; proof of Lemma 8.1 corrected; discussion of case \kappa_* =1 in the proof of Theorem 2 corrected with new Lemma A.2; accepted for publication in Comm. Pure. Appl. Mat

Uniqueness and Nondegeneracy of Ground States for (−Δ)sQ+Q−Qα+1=0(-\Delta)^s Q + Q - Q^{\alpha+1} = 0 in R\mathbb{R}

We prove uniqueness of ground state solutions $Q = Q(|x|) \geq 0$ for the nonlinear equation $(-\Delta)^s Q + Q - Q^{\alpha+1}= 0$ in $\mathbb{R}$, where $0 < s < 1$ and $0 < \alpha < \frac{4s}{1-2s}$ for $s < 1/2$ and $0 < \alpha < \infty$ for $s \geq 1/2$. Here $(-\Delta)^s$ denotes the fractional Laplacian in one dimension. In particular, we generalize (by completely different techniques) the specific uniqueness result obtained by Amick and Toland for $s=1/2$ and $\alpha=1$ in [Acta Math., \textbf{167} (1991), 107--126]. As a technical key result in this paper, we show that the associated linearized operator $L_+ = (-\Delta)^s + 1 - (\alpha+1) Q^\alpha$ is nondegenerate; i.\,e., its kernel satisfies $\mathrm{ker}\, L_+ = \mathrm{span}\, \{Q'\}$. This result about $L_+$ proves a spectral assumption, which plays a central role for the stability of solitary waves and blowup analysis for nonlinear dispersive PDEs with fractional Laplacians, such as the generalized Benjamin-Ono (BO) and Benjamin-Bona-Mahony (BBM) water wave equations.Comment: 45 page

Vida postcosecha de frutos de jiotilla sometidos a golpeo

La jiotilla es una cactácea mexicana, cuyos frutos se cosechan manualmente y pueden sufrir daños por golpeo, lo cual afectan su comercialización y modifican su vida postcosecha. Por lo que el objetivo del trabajo fue evaluar el daño por golpeo (0, 1, 2 y 4 m de altura) mediante peso, firmeza, color, azúcares totales y reductores en frutos de jiotilla cosechados en Coxcatlán, Puebla. Las variables se registraron los días 1, 3, 5 y 7 después de cosechados. El golpeo provocó disminución del 22.53 y 87.31 % en el peso y la firmeza respectivamente. Los parámetros de color L* y C* presentaron disminución del 25 y 50 %, respectivamente, mientras el parámetro h° presentó color amarillo al inicio y rojo al final. Los azúcares totales y reductores presentaron un coeficiente de variación del 44 y 69 %. El golpeo provocó una disminución del peso y firmeza, importantes para el manejo postcosecha del fruto.The jiotilla is a Mexican cactus, whose fruits are harvested manually and can be damaged by beating, which affects their commercialization and modifies their post-harvest life. So, the objective of the work was to evaluate the damage by hitting (0, 1, 2, and 4 m height) by weight, firmness, color, total sugars and reducers in jiotilla fruits harvested in Coxcatlán, Puebla. The variables were recorded on days 1, 3, 5 and 7 after harvesting. The hit caused a decrease of 22.53 and 87.31 % in weight and firmness, respectively. The color parameters L * and C * showed a decrease of 25 and 50 %, respectively, while the h º parameter showed yellow at the beginning and red at the end. The total and reducing sugars showed a coefficient of variation of 44 and 69 %. The hit caused a decrease in weight and firmness, important for the postharvest handling of the fruit

Calcio y cobalto en soluciones preservantes durante la vida postcosecha de tallos de Lily: cambios en las variables ornamentales

Dentro de los productos hortícolas, las flores de corte son de los más perecederos, por lo que durante su vida postcosecha se utilizan soluciones preservantes para mejorar su estado ornamental, las incluyen azúcar, un acidificante, un antiséptico y retardadores del metabolismo. En este trabajo se adicionaron cobalto y calcio en soluciones preservantes y se evaluaron las variables de consumo de solución, cambios de peso durante la vida postcosecha y vida de florero en tallos de Lily “Star Gazer” y “Star Fighter”. El cobalto actúa como antiséptico, mientras que el calcio permite dar estabilidad a la membrana celular. Se estableció un diseño factorial completamente al azar. Los resultados óptimos se observaron en el tratamiento de 0.5 mM de calcio, adicionado con 0.1 mM de Cobalto. Lo cual permitió establecer que la presencia de cobalto y calcio favoreció el retraso de los síntomas de la senescencia en tallos de LiliumAmong horticultural products, cut flowers are among the most perishable, so during their postharvest life preservative solutions are used to improve their ornamental state, including sugar, an acidifier, an antiseptic and metabolism retarder. In this work, cobalt and calcium were added in preservative solutions and the variables of solution consumption, weight changes during postharvest life and vase life in stems of Lily "Star Gazer" and "Star Fighter" were evaluated. Cobalt acts as an antiseptic, while calcium provides stability to the cell membrane. A completely random factorial design was established. The optimal results were observed in the treatment of 0.5 mM of calcium, added with 0.1 mM of Cobalt. This allowed establishing that the presence of cobalt and calcium favored the delay of the symptoms of senescence in Lilium stems

Pruning height and frequency of Moringa oleifera and Leucaena leucocephala in a silvopastoral system

Objetive: Evaluate two heights (50 and 70 cm) and pruning frequencies (60 and 135 d) in Moringa oleifera and Leucaena leucocephala in a developing silvopastoral system. Desing/methodology/approach: Four treatments were established, T1: Moringa oleifera with pruning at 50 cm, T2: Moringa oleifera with pruning at 70 cm, T3: Leucaena leucocephala with pruning at 50 cm and T4: Leucaena leucocephala with pruning at 70 cm and pruning frequencies at the 60 and 135 d. The number of sprouts, diameter and length of the largest sprout, and biomass were recorded. The data were analyzed using a mixed model, analysis of variance and Tukey's tests. Results: The number of regrowths in L. leucocephala was higher than M. oleifera. The T2 had the highest behavior at 60 d, for L. leucocephala it was similar between pruning and frequencies. The diameter and length were greater for T2 at both frequencies, at 60 d for T3 and at 135 d for T4. Biomass was higher in M. oleífera than L. leucocephala, pruning at 70 cm was better than at 50 cm. Pruning at 135 days obtained higher biomass than at 60 days. T2 obtained higher biomass at 60 d, T1 and T4 at 135 d. Study limitations/implications: Forage species, frequencies and pruning heights determine the growth potential and amount of biomass available to the animals. Findings/conclusions:Leucaena leucocephala has better agronomic performance in response to pruning without influencing the height and frequency of pruning in a silvopastoral system.Objective: To evaluate two different heights (50 and 70 cm) and pruning frequencies (60 and 135 days) in Moringa oleifera and Leucaena leucocephala in a developing silvopastoral system. Design/methodology/approach: Four treatments were established: T1=Moringa oleifera with pruning at 50 cm; T2=Moringa oleifera with pruning at 70 cm; T3=Leucaena leucocephala with pruning at 50 cm; and T4=Leucaena leucocephala with pruning at 70 cm. In all cases, pruning frequencies were 60 and 135 days. The number of sprouts, diameter, and length of the largest sprout, as well as the amount of biomass, were recorded. A mixed model, variance analysis, and Tukey's test were used to analyze the data. Results: The number of regrowths for L. leucocephala was higher than for M. oleifera. Treatment T2 had the highest performance at day 60; in the case of L. leucocephala, performance was similar between pruning frequencies. For T2, diameter and length were larger at both frequencies; for T3, at 60 days; and for T4, at 135 days. Biomass was higher for M. oleifera than for L. leucocephala, while pruning at 70 cm was better than at 50 cm. Pruning at 135 days produced a higher biomass than at 60 days. For T2, biomass was higher at 60 days, while for T1 and T4, it was higher at 135 days. Study limitations/implications: Forage species, as well as pruning frequencies and heights, determine tree growth potential and the amount of biomass available for animals. Findings/conclusions: The agronomic performance of Leucaena leucocephala has a better response to pruning, regardless of pruning height and frequency, in a silvopastoral system

Blockchains for Business Process Management - Challenges and Opportunities

Blockchain technology promises a sizable potential for executing inter-organizational business processes without requiring a central party serving as a single point of trust (and failure). This paper analyzes its impact on business process management (BPM). We structure the discussion using two BPM frameworks, namely the six BPM core capabilities and the BPM lifecycle. This paper provides research directions for investigating the application of blockchain technology to BPM.Comment: Preprint for ACM TMI

Bioaccessibility of selenium after human ingestion in relation to its chemical species and compartmentalization in maize

International audienceSelenium is a micronutrient needed by all living organisms including humans, but often present in low concentration in food with possible deficiency. From another side, at higher concentrations in soils as observed in seleniferous regions of the world, and in function of its chemical species, Se can also induce (eco)toxicity. Root Se uptake was therefore studied in function of its initial form for maize (Zea mays L.), a plant widely cultivated for human and animal food over the world. Se phytotoxicity and compartmentalization were studied in different aerial plant tissues. For the first time, Se oral human bioaccessibility after ingestion was assessed for the main Se species (SeIV and SeVI) with the BARGE ex vivo test in maize seeds (consumed by humans), and in stems and leaves consumed by animals. Corn seedlings were cultivated in hydroponic conditions supplemented with 1 mg L−1 of selenium (SeIV, SeVI, Control) for 4 months. Biomass, Se concentration, and bioaccessibility were measured on harvested plants. A reduction in plant biomass was observed under Se treatments compared to control, suggesting its phytotoxicity. This plant biomass reduction was higher for selenite species than selenate, and seed was the main affected compartment compared to control. Selenium compartmentalization study showed that for selenate species, a preferential accumulation was observed in leaves, whereas selenite translocation was very limited toward maize aerial parts, except in the seeds where selenite concentrations are generally high. Selenium oral bioaccessibility after ingestion fluctuated from 49 to 89 % according to the considered plant tissue and Se species. Whatever the tissue, selenate appeared as the most human bioaccessible form. A potential Se toxicity was highlighted for people living in seleniferous regions, this risk being enhanced by the high Se bioaccessibility

Potassium and Sodium Transport in Yeast

[EN] As the proper maintenance of intracellular potassium and sodium concentrations is vital for cell growth, all living organisms have developed a cohort of strategies to maintain proper monovalent cation homeostasis. In the model yeast Saccharomyces cerevisiae, potassium is accumulated to relatively high concentrations and is required for many aspects of cellular function, whereas high intracellular sodium/potassium ratios are detrimental to cell growth and survival. The fact that S. cerevisiae cells can grow in the presence of a broad range of concentrations of external potassium (10 M–2.5 M) and sodium (up to 1.5 M) indicates the existence of robust mechanisms that have evolved to maintain intracellular concentrations of these cations within appropriate limits. In this review, current knowledge regarding potassium and sodium transporters and their regulation will be summarized. 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