Scattering of the three-dimensional cubic nonlinear Schr\"odinger equation with partial harmonic potentials

In this paper, we consider the following three dimensional defocusing cubic nonlinear Schr\"odinger equation (NLS) with partial harmonic potential \begin{equation*}\tag{NLS} i\partial_t u + \left(\Delta_{\mathbb{R}^3 }-x^2 \right) u = |u|^2 u, \quad u|_{t=0} = u_0. \end{equation*} Our main result shows that the solution $u$ scatters for any given initial data $u_0$ with finite mass and energy. The main new ingredient in our approach is to approximate (NLS) in the large-scale case by a relevant dispersive continuous resonant (DCR) system. The proof of global well-posedness and scattering of the new (DCR) system is greatly inspired by the fundamental works of Dodson \cite{D3,D1,D2} in his study of scattering for the mass-critical nonlinear Schr\"odinger equation. The analysis of (DCR) system allows us to utilize the additional regularity of the smooth nonlinear profile so that the celebrated concentration-compactness/rigidity argument of Kenig and Merle applies.Comment: 71 page

Scattering of the three-dimensional cubic nonlinear Schrödinger equation with partial harmonic potentials

In this paper, we consider the following three dimensional defocusing cubic nonlinear Schrödinger equation (NLS) with partial harmonic potential \begin{equation} \left\{\begin{array}{l} i\partial_tu + \left(\Delta_{\mathbb{R}^3}-x^2\right)u = |u|^2u, \\ u|_{t=0} = u_0 \\ \end{array}\right. \tag{NLS} \end{equation} Out main result shows that the solution $u$ scatters for any given initial data $u_0$ with finite mass and energy. The main new ingredient in our approach is to approxmate (NLS) in the large-scale case by a relevant dispersive continuous resonant (DCR) system. The proof of global well-posedness and scattering of the new (DCR) system is greatly inspired by the fundamental works of Dodson [29, 31, 32] in his study of scattering for the mass-critical nonlinear Schrödinger equation. The analysis of (DCR) system allows us to utilize the additional regularity of the smooth nonlinear profile so that the celebrated concentration-compactness/rigidity argument of Kenig and Merle [61,62] applies

Backbone phylogeny and adaptive evolution of Pleurospermum s. l.: New insights from phylogenomic analyses of complete plastome data

Pleurospermum is a taxonomically challenging taxon of Apiaceae, as its circumscription and composition remain controversial for morphological similarities with several related genera, leading to a dispute between Pleurospermum in the broad sense and strict sense. While evidence from previous molecular studies recognized plural branching lineages within the Pleurospermum s. l., it did not support the latest delimitation of Pleurospermum s. str. by only two closely related northern species. So far, no proper delimitation for Pleurospermum has come up, and many of the plural taxa in Pleurospermum s. l. remain unresolved, which may be due to poor phylogenetic resolution yielded barely from ITS sequences. Herein, we newly assembled 40 complete plastomes from 36 species of Pleurospermum s. l. and related genera, 34 of which were first reported and generated a well-resolved backbone phylogeny in a framework of the subfamily Apioideae. From the phylogeny with greatly improved resolution, a total of six well-supported monophyletic lineages within Pleurospermum s. l. were recognized falling in different major clades of Apioideae. Combining morphological characteristics with phylogenetic inference, we suggested to re-delimit the Pleurospermum s. str. by introducing nine species mainly from the Himalayan regions and proposed its boundary features; the remaining species were suggested to be excluded from Pleurospermum to incorporate into their more related taxa being revealed. On this basis, the plastome comparison revealed not only the high conservatism but also the mild differences among lineages in plastome structure and gene evolution. Overall, our study provided a backbone phylogeny essential for further studies of the taxonomically difficult taxa within Pleurospermum s. l

Clearance of Free Silica in Rat Lungs by Spraying with Chinese Herbal Kombucha

The effects of spraying with kombucha and Chinese herbal kombucha were compared with treatments with tetrandrine in a rat silicosis model. Silica dust (50 mg) was injected into the lungs of rats, which were then treated with one of the experimental treatments for a month. The rats were then killed and the effects of the treatments were evaluated by examining the extent and severity of the histopathological lesions in the animals’ lungs, measuring their organ coefficients and lung collagen contents, determining the dry and wet weights of their lungs, and measuring the free silica content of the dried lungs. In addition, lavage was performed on whole lungs taken from selected rats, and the numbers and types of cells in the lavage fluid were counted. The most effective treatment in terms of the ability to reduce lung collagen content and minimize the formation of pulmonary histopathological lesions was tetrandrine treatment, followed by Chinese herbal kombucha and non-Chinese herbal kombucha. However, the lavage fluid cell counts indicated that tetrandrine treatment had severe adverse effects on macrophage viability. This effect was much less pronounced for the kombucha and Chinese herbal kombucha treatments. Moreover, the free silica levels in the lungs of animals treated with Chinese herbal kombucha were significantly lower than those for any other silica-exposed group. These preliminary results indicate that spraying with Chinese herbal kombucha preparations can effectively promote the discharge of silica dust from lung tissues. Chinese herbal kombucha inhalation may thus be a useful new treatment for silicosis and other pneumoconiosis diseases

Pb(II)-inducible proviolacein biosynthesis enables a dual-color biosensor toward environmental lead

With the rapid development of synthetic biology, various whole-cell biosensors have been designed as valuable biological devices for the selective and sensitive detection of toxic heavy metals in environmental water. However, most proposed biosensors are based on fluorescent and bioluminescent signals invisible to the naked eye. The development of visible pigment-based biosensors can address this issue. The pbr operon from Klebsiella pneumoniae is selectively induced by bioavailable Pb(II). In the present study, the proviolacein biosynthetic gene cluster was transcriptionally fused to the pbr Pb(II) responsive element and introduced into Escherichia coli. The resultant biosensor responded to Pb(II) in a time- and dose-dependent manner. After a 5-h incubation with Pb(II), the brown pigment was produced, which could be extracted into n-butanol. Extra hydrogen peroxide treatment during n-butanol extract resulted in the generation of a stable green pigment. An increased brown signal was observed upon exposure to lead concentrations above 2.93 nM, and a linear regression was fitted from 2.93 to 3,000 nM. Extra oxidation significantly decreased the difference between parallel groups. The green signal responded to as low as 0.183 nM Pb(II), and a non-linear regression was fitted in a wide concentration range from 0.183 to 3,000 nM. The specific response toward Pb(II) was not interfered with by various metals except for Cd(II) and Hg(II). The PV-based biosensor was validated in monitoring bioaccessible Pb(II) spiked into environmental water. The complex matrices did not influence the regression relationship between spiked Pb(II) and the dual-color signals. Direct reading with the naked eye and colorimetric quantification enable the PV-based biosensor to be a dual-color and low-cost bioindicator for pollutant heavy metal

Clearance of Free Silica in Rat Lungs by Spraying with Chinese Herbal Kombucha

The effects of spraying with kombucha and Chinese herbal kombucha were compared with treatments with tetrandrine in a rat silicosis model. Silica dust (50 mg) was injected into the lungs of rats, which were then treated with one of the experimental treatments for a month. The rats were then killed, and the effects of the treatments were evaluated by examining the extent and severity of the histopathological lesions in the animals’ lungs, measuring their organ coefficients and lung collagen contents, determining the dry and wet weights of their lungs, and measuring the free silica content of the dried lungs. In addition, lavage was performed on whole lungs taken from selected rats, and the numbers and types of cells in the lavage fluid were counted. The most effective treatment in terms of the ability to reduce lung collagen content and minimize the formation of pulmonary histopathological lesions was tetrandrine treatment, followed by Chinese herbal kombucha and non‐Chinese herbal kombucha. However, the lavage fluid cell counts indicated that tetrandrine treatment had severe adverse effects on macrophage viability. This effect was much less pronounced for the kombucha and Chinese herbal kombucha treatments. Moreover, the free silica levels in the lungs of animals treated with Chinese herbal kombucha were significantly lower than those for any other silica‐exposed group. These preliminary results indicate that spraying with Chinese herbal kombucha preparations can effectively promote the discharge of silica dust from lung tissues. Chinese herbal kombucha inhalation may thus be a useful new treatment for silicosis and other pneumoconiosis diseases