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In this article, we study mass-critical stochastic nonlinear Schrödinger equations with a multiplicative noise in 3D with a slight time decay (⁠|$\langle t \rangle ^{-\epsilon }$| for |$\epsilon>0$| arbitrarily small). We prove associated global space-time bounds and the scattering behavior. [ABSTRACT FROM AUTHOR]

In this article, we study the log-log blowup dynamics for the mass critical nonlinear Schrödinger equation on R² under rough but structured random perturbations at L².R²/ regularity. In particular, by employing probabilistic methods, we provide a construction of a family of L².R²/ regularity solutions which do not lie in Hs.R²/ for any s > 0, and which blowup according to the log-log dynamics. [ABSTRACT FROM AUTHOR]

We prove the global space-time bound for the defocusing mass critical nonlinear Schrödinger equation on R 3 perturbed by a small multiplicative noise. The associated scattering behavior is also obtained. In addition to techniques from Fan and Xu (Global well-posedness for the defocusing mass-critical stochastic nonlinear Schrödinger equation on R at L 2 regularity, 2018) and Fan and Zhao (On long time behavior for stochastic nonlinear Schrödinger equations with a multiplicative noise, 2020), the main new ingredients are the decomposition of the solution tailored for the bootstrap argument in this problem, and the incorporation of local smoothing norms to close the argument. We also prove the global space-time Strichartz estimate for the linear stochastic equation. It is a toy model of our nonlinear problem, but the bound itself is new and of its own interest. Furthermore, the proof we give for the linear model is more direct, and also illustrates the proof strategy for the nonlinear problem. [ABSTRACT FROM AUTHOR]

In this note, we show the existence of a special solution u to defocusing cubic NLS in 3d, which lives in H^{s} for all s>0, but scatters to a linear solution in a very slow way. We prove for this u, for all \epsilon >0, one has \sup _{t>0}t^{\epsilon }\|u(t)-e^{it\Delta }u^{+}\|_{\dot {H}^{1/2}}=\infty. Note that such a slow asymptotic convergence is impossible if one further pose the initial data of u(0) be in L^{1}. We expect that similar construction hold the for other NLS models. It can been seen the slow convergence is caused by the fact that there are delayed backward scattering profile in the initial data, we also illustrate why L^{1} condition of initial data will get rid of this phenomena. [ABSTRACT FROM AUTHOR]

We study the non-scattering |$L^{2}$| solution |$u$| to the radial focusing mass-critical nonlinear Schrödinger equation with mass just above the ground state, and show that there exists a time sequence |$\{t_{n}\}_{n}$|⁠ , such that |$u(t_{n})$| weakly converges to the ground state |$Q$| up to scaling and phase transformation. We also give some partial results on the mass concentration phenomena of the minimal mass blow-up solution. [ABSTRACT FROM AUTHOR]

We show robustness of various truncated and subcritical approximations to the stochastic defocusing mass-critical nonlinear Schrödinger equation (NLS) in dimension d = 1 , whose solution was constructed in [8] with one particular such approximation. The key ingredient in the proof is a uniform bound of the solutions to the family of deterministic mass-subcritical defocusing NLS. [ABSTRACT FROM AUTHOR]

We study the focusing mass-critical nonlinear Schrödinger equation, and construct certain solutions which blow up at exactly m points according to the log–log law. [ABSTRACT FROM AUTHOR]

We present a novel approach to control the blending of line and polygon skeleton-based convolution surfaces using locally varying Ratio of Support radius and Thickness (RST). With our method, solutions for local convolution surface approximation with prescribed surface thickness and support radii can be derived analytically. In addition, iso-surface shrinkage can be avoided by offsetting the endpoints of line skeletons and the edges of polygon skeletons. Our RST-based blending for convolution surfaces is local and can generate desired blending effects while approximating shapes with a specified thickness. Moreover, our method is intuitive and users can control the blending by adjusting the skeletal radius or the support radius of the finite support kernel independently. As our blending utilizes convolution integration only without requiring any extra composition operators, it allows for successive convolution blending operations to create complex shapes. [Display omitted] • Blending control for convolution surfaces using locally varying RSTs. • Analytical solutions for surface thickness approximation with prescribed RSTs. • Numerical solutions for approximating the skeleton boundaries with given RSTs. [ABSTRACT FROM AUTHOR]

Background: Various environmental factors are capable of oxidative stress to result in limiting plant development and agricultural production. Fullerene-based carbon nanomaterials can enable radical scavenging and positively regulate plant growth. Even so, to date, our knowledge about the mechanism of fullerene-based carbon nanomaterials on plant growth and response to oxidative stress is still unclear. Results: 20 or 50 mg/L quaternary ammonium iminofullerenes (IFQA) rescued the reduction in root lengths and root-hair densities and lengths of Arabidopsis and maize induced by accumulation of endogenous hydrogen peroxide (H2O2) under 3-amino-1,2,4-triazole or exogenous H2O2 treatment, as well as the root active absorption area and root activity under exogenous H2O2 treatment. Meanwhile, the downregulated contents of ascorbate acid (ASA) and glutathione (GSH) and the upregulated contents of dehydroascorbic acid (DHA), oxidized glutathione (GSSG), malondialdehyde (MDA), and H2O2 indicated that the exogenous H2O2 treatment induced oxidative stress of maize. Nonetheless, application of IFQA can increase the ratios of ASA/DHA and GSH/GSSG, as well as the activities of glutathione reductase, and ascorbate peroxidase, and decrease the contents of H2O2 and MDA. Moreover, the root lengths were inhibited by buthionine sulfoximine, a specific inhibitor of GSH biosynthesis, and subsequently rescued after addition of IFQA. The results suggested that IFQA could alleviate exogenous-H2O2-induced oxidative stress on maize by regulating the ASA-GSH cycle. Furthermore, IFQA reduced the excess accumulation of ROS in root hairs, as well as the NADPH oxidase activity under H2O2 treatment. The transcript levels of genes affecting ROS-mediated root-hair development, such as RBOH B, RBOH C, PFT1, and PRX59, were significantly induced by H2O2 treatment and then decreased after addition of IFQA. Conclusion: The positive effect of fullerene-based carbon nanomaterials on maize-root-hair growth under the induced oxidative stress was discovered. Application IFQA can ameliorate oxidative stress to promote maize-root growth through decreasing NADPH-oxidase activity, improving the scavenging of ROS by ASA-GSH cycle, and regulating the expressions of genes affecting maize-root-hair development. It will enrich more understanding the actual mechanism of fullerene-based nanoelicitors responsible for plant growth promotion and protection from oxidative stress. [ABSTRACT FROM AUTHOR]

Calcineurin B-like proteins (CBLs) as specific calcium sensors that interact with CBL-interacting protein kinases (CIPKs) play a key role in the regulation of plant development and abiotic stress tolerance. In this study, we isolated and characterized the CIPK32 gene from Zea mays. ZmCIPK32 showed that it comprised 440 amino acids and a conserved NAF motif responsible for the interaction with CBLs localized in the cytoplasm and cell membrane. The interaction of ZmCIPK32 with ZmCBL1 and ZmCBL9 demonstrated using yeast two-hybrid system and bimolecular fluorescence complementation assay required the presence of the NAF domain. Overexpression of ZmCIPK32 promoted early germination in transgenic Arabidopsis seeds relative to that observed in wild-type (WT) plants under mannitol treatment. In addition, ZmCIPK32 -overexpressing plants were insensitive to treatments with exogenous abscisic acid and paclobutrazol (PBZ) at seed germination and early seedling stages. Expression levels of the key genes GA20ox and GA3ox involved in the synthesis of gibberellin (GA) were increased, whereas expression levels of genes involved in the conversion of active GA to inactive forms and GA signaling were reduced in ZmCIPK32- overexpressing plants relative to those in WT plants under mannitol and PBZ treatments. Furthermore, overexpression of ZmCIPK32 increased GA level but decreased abscisic acid level in transgenic lines compared to the respective levels in WT plants under PBZ or mannitol treatments. Our results suggest that ZmCIPK32 positively regulates seed germination under stressed conditions by modulating GA signals. • The expressions of ZmCIPK32 were regulated by GA and PBZ treatments during seed germination. • ZmCIPK32 interacted with ZmCBL1 and ZmCBL9 in vivo. • ZmCIPK32 regulated expression of genes for GA metabolism, GA and ABA contents during seed germination under stress. • ZmCIPK32 regulated GA signals to promote seed germination under stresses. [ABSTRACT FROM AUTHOR]