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The well-posedness of stochastic Navier–Stokes equations with various noises is a hot topic in the area of stochastic partial differential equations. Recently, the consideration of stochastic Navier–Stokes equations involving fractional Laplacian has received more and more attention. Due to the scaling-invariant property of the fractional stochastic equations concerned, it is natural and also very important to study the well-posedness of stochastic fractional Navier–Stokes equations in the associated critical Fourier–Besov spaces. In this paper, we are concerned with the three-dimensional stochastic fractional Navier–Stokes equation driven by multiplicative noise. We aim to establish the well-posedness of solutions of the concerned equation. To this end, by utilising the Fourier localisation technique, we first establish the local existence and uniqueness of the solutions in the critical Fourier–Besov space$$\dot{\mathcal {B}}^{4-2\alpha -\frac{3}{p}}_{p,r}$$${\dot{B}}_{p,r}^{4-2\alpha -\frac{3}{p}}$. Then, under the condition that the initial date is sufficiently small, we show the global existence of the solutions in the probabilistic sense.

 

Amyloid aggregation and microbial infection are considered as pathological risk factors for developing amyloid diseases, including Alzheimer's disease (AD), type II diabetes (T2D), Parkinson's disease (PD), and medullary thyroid carcinoma (MTC). Due to the multifactorial nature of amyloid diseases, single-target drugs and treatments have mostly failed to inhibit amyloid aggregation and microbial infection simultaneously, thus leading to marginal benefits for amyloid inhibition and medical treatments. Herein, we proposed and demonstrated a new “anti-amyloid and antimicrobial hypothesis” to discover two host-defense antimicrobial peptides of α-defensins containing β-rich structures (human neutrophil peptide of HNP-1 and rabbit neutrophil peptide of NP-3A), which have demonstrated multi-target, sequence-independent functions to (i) prevent the aggregation and misfolding of different amyloid proteins of amyloid-β (Aβ, associated with AD), human islet amyloid polypeptide (hIAPP, associated with T2D), and human calcitonin (hCT, associated with MTC) at sub-stoichiometric concentrations, (ii) reduce amyloid-induced cell toxicity, and (iii) retain their original antimicrobial activity upon the formation of complexes with amyloid peptides. Further structural analysis showed that the sequence-independent amyloid inhibition function of α-defensins mainly stems from their cross-interactions with amyloid proteins via β-structure interactions. The discovery of antimicrobial peptides containing β-structures to inhibit both microbial infection and amyloid aggregation greatly expands the new therapeutic potential of antimicrobial peptides as multi-target amyloid inhibitors for better understanding pathological causes and treatments of amyloid diseases. 

Ethylene complexes of gold( i ) have been stabilized by electron-rich, κ 2 -bound tris(pyrazolyl)borate ligands. Large up-field shifts of olefinic carbon NMR resonances and relatively long CC distances of gold bound ethylene are indicative of significant Au( i ) → ethylene π-backbonding relative to the analog supported by a weakly donating ligand, consistent with the computational data. 

Stimuli-responsive hydrogel strain sensors that synergize the advantages of both soft-wet hydrogels and smart functional materials have attracted rapidly increasing interest for exploring the opportunities from material design principles to emerging applications in electronic skins, health monitors, and human–machine interfaces. Stimuli-responsive hydrogel strain sensors possess smart and on-demand ability to specifically recognize various external stimuli and convert them into strain-induced mechanical, thermal, optical, and electrical signals. This review presents an up-to-date summary over the past five years on hydrogel strain sensors from different aspects, including material designs, gelation/fabrication methods, stimuli-responsive principles, and sensing performance. Hydrogel strain sensors are classified into five major categories based on the nature of the stimuli, and representative examples from each category are carefully selected and discussed in terms of structures, response mechanisms, and potential medical applications. Finally, current challenges and future perspectives of hydrogel strain sensors are tentatively proposed to stimulate more and better research in this emerging field.