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In this article, we mainly prove low regularity conservation laws for the Fokas-Lenells equation in Besov spaces with small initial data both on the line and on the circle. We develop a new technique in Fourier analysis and complex analysis to obtain the a priori estimates. It is based on the perturbation determinant associated with the Lax pair introduced by Killip, Vişan, and Zhang for completely integrable dispersive partial differential equations. Additionally, we also utilize the perturbation determinant to derive the global a priori estimates for the Schwartz solutions to the Camassa-Holm (CH) equation in H1{H}^{1}. Even though the energy conservation law of the CH equation is a fact known to all, the perturbation determinant method indicates that we cannot get any conserved quantities for the CH equation in Hk{H}^{k} except k=1k=1.

The effects of adding different amounts (0.1%, 0.2%, 0.3%, 0.4% and 0.5%) of psyllium husk powder (PHP), gellan gum (GG) or konjac glucomannan (KGM) on the properties of phosphorylated surimi-crab meat mixed gels (MG) were investigated. The gel properties were improved by adding a small amount (0.1%) of PHP or GG. With increasing addition level of hydrophilic colloids, phase separation occurred, so that the gel properties did not significantly change and even began to decrease. However, the addition of KGM had no significant effect on the breaking force or gel strength, and no phase separation was observed under laser scanning confocal microscopy (LSCM). The addition of PHP and GG increased the temperature at which G’ began to decrease, which was beneficial to the improvement of gel properties. The denaturation of myosin required higher temperature and less energy in the phosphorylated MG system with hydrophilic colloids, and temperature may become a major influential factor in the denaturation process. The overall structural stability of proteins in MG was enhanced by adding a small amount of PHP or KGM. However, PHP and GG had a destructive effect on actin. On the contrary, the addition of a small amount of KGM could increase the structural stability of actin, which may be unfavorable for the formation of gels. The interaction between myosin and actin in the MG system was conducive to enhancing the overall structural stability of proteins. The three hydrophilic colloids, especially GG, at an addition level of 0.1% was beneficial to the improvement of gel properties. The incorporation of hydrophilic colloids may be a novel strategy to improve the quality of phosphorylated MG.

The development of single-cell RNA sequencing (scRNA-seq) has allowed high-resolution analysis of cell-type diversity and transcriptional networks controlling cell-fate specification. To identify the transcriptional networks governing human retinal development, we performed scRNA-seq analysis on 16 time points from developing retina as well as four early stages of retinal organoid differentiation. We identified evolutionarily conserved patterns of gene expression during retinal progenitor maturation and specification of all seven major retinal cell types. Furthermore, we identified gene-expression differences between developing macula and periphery and between distinct populations of horizontal cells. We also identified species-specific patterns of gene expression during human and mouse retinal development. Finally, we identified an unexpected role for ATOH7 expression in regulation of photoreceptor specification during late retinogenesis. These results provide a roadmap to future studies of human retinal development and may help guide the design of cell-based therapies for treating retinal dystrophies.

This paper considers the generalized sectorial decompositions of semi-sectorial operators and quasi-sectorial operators on the complex Hilbert space. Under an invariant subspace condition, a necessary and sufficient condition for the existence of the generalized sectorial decomposition of a semi-sectorial operator is given. The generalized sectorial decomposition of a quasi-sectorial operator is given without any conditions. Some sufficient conditions for a block upper triangular operator matrix to be a semi-sectorial operator or a quasi-sectorial operator are given. [ABSTRACT FROM AUTHOR]

Motivated by new examples of functional Banach spaces over the unit disk, arising as the symbol spaces in the study of random analytic functions, for which the monomials $\{z^n\}_{n\geq 0}$ exhibit features of an unconditional basis yet they often don't even form a Schauder basis, we introduce a notion called solid basis for Banach spaces and p -Banach spaces and study its properties. Besides justifying the rich existence of solid bases, we study their relationship with unconditional bases, the weak-star convergence of Taylor polynomials, the problem of a solid span and the curious roles played by c 0. The two features of this work are as follows: (1) during the process, we are led to revisit the axioms satisfied by a typical Banach space of analytic functions over the unit disk, leading to a notion of $\mathcal{X}^\mathrm{max}$ (and $\mathcal{X}^\mathrm{min}$), as well as a number of related functorial constructions, which are of independent interests; (2) the main interests of solid basis lie in the case of non-separable (p -)Banach spaces, such as BMOA and the Bloch space instead of VMOA and the little Bloch space. [ABSTRACT FROM AUTHOR]

This paper deals with the converse problems about the robust stability of finite dimensional negative imaginary systems. Various converse negative imaginary theorems are established for linear time-invariant systems. It is shown that the feedback interconnection stability of a specific system with an arbitrary strictly negative imaginary system implies the negative imaginary property of the specific. [ABSTRACT FROM AUTHOR]

Utilizing thermal updrafts shows potential for enabling long-endurance cruising of fixed-wing unmanned aerial vehicles without energy consumption. This article presents a novel online method based on sparse identification of nonlinear dynamics (SINDy) approach to achievement identification of thermal sources in the atmosphere. Initially, the algorithm is incorporated into the upper-level planning system, interacting with the lower-level controller. Then, experiments are conducted through software-in-the-loop simulations (SITL) to validate the implementation of the proposed algorithm. It is found that direct observation of thermal sources through measurements using SINDy is unfeasible during straight and circular flight modes. Nevertheless, simulation analysis of the proposed approach indicates that under unobservable conditions, a portion of the parameters can still be identified. By comparing results obtained using the particle filter algorithm, this method is shown to accurately estimate the parameters with negligible errors under observability conditions. The novelty of this approach lies in its significant improvement of the localization accuracy of the thermal source, without the need for parameter adjustments in the algorithm. Finally, the proposed methods are integrated into commonly used hardware platforms, and their online feasibility is verified through hardware-in-the-loop simulations. [ABSTRACT FROM AUTHOR]

We establish the Bonnet–Myers theorem, Laplacian comparison theorem, and Bishop–Gromov volume comparison theorem for weighted Finsler manifolds as well as weighted Finsler spacetimes, of weighted Ricci curvature bounded below by using the weight function. These comparison theorems are formulated with ϵ-range introduced in our previous paper, that provides a natural viewpoint of interpolating weighted Ricci curvature conditions of different effective dimensions. Some of our results are new even for weighted Riemannian manifolds and generalize comparison theorems of Wylie–Yeroshkin and Kuwae–Li.