一类非线性椭圆方程的刘维尔型定理

设（Mⁿ,g）是一个n维非紧的完备黎曼流行.本文考虑有正解的非线性椭圆方程△_fu+au log u=0的刘维尔型定理,其中a是一个非零常数.利用Bochner公式和极大值原理,获得了以上方程在Bakry-Emery里奇曲率有下界时正解的Li-Yau型梯度估计和某些有关的刘维尔理论,推广了文献[7]的结果.     

Numerical Studies on Asymptotics of European Option Under Multiscale Stochastic Volatility

Multiscale stochastic volatilities models relax the constant volatility assumption from Black-Scholes option pricing model. Such models can capture the smile and skew of volatilities and therefore describe more accurately the movements of the trading prices. Christoffersen et al. Manag Sci 55(2):1914–1932 (2009) presented a model where the underlying price is governed by two volatility components, one changing fast and another changing slowly. Chiarella and Ziveyi Appl Math Comput 224:283–310 (2013) transformed Christoffersen’s model and computed an approximate formula for pricing American options. They used Duhamel’s principle to derive an integral form solution of the boundary value problem associated to the option price. Using method of characteristics, Fourier and Laplace transforms, they obtained with good accuracy the American option prices. In a previous research of the authors (Canhanga et al. 2014), a particular case of Chiarella and Ziveyi Appl Math Comput 224:283–310 (2013) model is used for pricing of European options. The novelty of this earlier work is to present an asymptotic expansion for the option price. The present paper provides experimental and numerical studies on investigating the accuracy of the approximation formulae given by this asymptotic expansion. We present also a procedure for calibrating the parameters produced by our first-order asymptotic approximation formulae. Our approximated option prices will be compared to the approximation obtained by Chiarella and Ziveyi Appl Math Comput 224:283–310 (2013).     

Evidence for Multiple Binding Modes in the Initial Contact Between SARS-CoV-2 Spike S1 Protein and Cell Surface Glycans**

Infection of host cells by SARS-CoV-2 begins with recognition by the virus S (spike) protein of cell surface heparan sulfate (HS), tethering the virus to the extracellular matrix environment, and causing the subunit S1-RBD to undergo a conformational change into the ‘open’ conformation. These two events promote the binding of S1-RBD to the angiotensin converting enzyme 2 (ACE2) receptor, a preliminary step toward viral-cell membrane fusion. Combining ligand-based NMR spectroscopy with molecular dynamics, oligosaccharide analogues were used to explore the interactions between S1-RBD of SARS CoV-2 and HS, revealing several low-specificity binding modes and previously unidentified potential sites for the binding of extended HS polysaccharide chains. The evidence for multiple binding modes also suggest that highly specific inhibitors will not be optimal against protein S but, rather, diverse HS-based structures, characterized by high affinity and including multi-valent compounds, may be required.     

Activatable NIR-II Photothermal Lipid Nanoparticles for Improved Messenger RNA Delivery

Endosomal escape remains a central issue limiting the high protein expression of mRNA therapeutics. Here, we present second near-infrared (NIR-II) lipid nanoparticles (LNPs) containing pH activatable NIR-II dye conjugated lipid (Cy-lipid) for potentiating mRNA delivery efficiency via a s timulus-responsive p hotothermal-promoted e ndosomal e scape d elivery (SPEED) strategy. In acidic endosomal microenvironment, Cy-lipid is protonated and turns on NIR-II absorption for light-to-heat transduction mediated by 1064 nm laser irradiation. Then, the heat-promoted LNPs morphology change triggers rapid escape of NIR-II LNPs from the endosome, allowing about 3-fold enhancement of enhanced green fluorescent protein (eGFP) encoding mRNA translation capacity compared to the NIR-II light free group. In addition, the bioluminescence intensity induced by delivered luciferase encoding mRNA in the mouse liver region shows positive correlation with incremental radiation dose, indicating the validity of the SPEED strategy.     

Reversible Solid–Solid Conversion of Sulfurized Polyacrylonitrile Cathodes in Lithium–Sulfur Batteries by Weakly Solvating Ether Electrolytes

Despite carbonate electrolytes exhibiting good stability to sulfurized polyacrylonitrile (SPAN), their chemical incompatibility with lithium (Li) metal anode leads to poor electrochemical performance of Li||SPAN full cells. While the SPAN employs conventional ether electrolytes that suffer from the shuttle effect, leading to rapid capacity fading. Here, we tailor a dilute electrolyte based on a low solvating power ether solvent that is both compatible with SPAN and Li metal. Unlike conventional ether electrolytes, the weakly solvating ether electrolyte enables SPAN to undergo reversibly “solid–solid” conversion. It features an anion–rich solvation structure that allows for the formation of a robust cathode electrolyte interphase on the SPAN, effectively blocking the dissolution of polysulfides into the bulk electrolyte and avoiding the shuttle effect. What's more, the unique electrolyte chemistry endowed Li ions with fast electroplating kinetics and induced high reversibility Li deposition/stripping process from 25 °C to −40 °C. Based on tailored electrolyte, Li||SPAN full cells matched with high loading SPAN cathodes (≈3.6 mAh cm⁻²) and 50 μm Li foil can operate stably over a wide range of temperatures. Additionally, Li||SPAN pouch cell under lean electrolyte and 5 % excess Li conditions can continuously operate stably for over a month.     

980 nm Photobiomodulation Promotes Osteo/Odontogenic Differentiation of the Stem Cells from Human Exfoliated Deciduous Teeth Via the Cross talk Between BMP/Smad and Wnt/β-Catenin Signaling Pathways

Increasing evidence suggests stem cells from human exfoliated deciduous teeth (SHEDs) serve as desirable sources of dentin regeneration. Photobiomodulation (PBM) has shown great potential in enhancing the proliferation and osteogenesis of human bone marrow mesenchymal stem cells (hBMMSCs). However, the specific role of PBM in odontogenic differentiation of SHEDs is little know, and we further investigated potential mechanism of PBM osteo/odontogenisis. A 980 nm diode laser with different energy densities of (0.5, 5, 10 J cm⁻²) in a 100-mW continuous wave was used for irradiation every 24 h. Osteo/odontogenic differentiation of SHEDs was achieved by performing alkaline phosphatase (ALP) and alizarin red staining (ARS) and osteo/odontogenic markers were also evaluated by qRT-PCR and western blotting. Additionally, western blot and immunohistochemical staining were performed to evaluate the levels of BMP/Smad and Wnt/β-catenin signaling-related proteins. We found that PBM at 5 J cm⁻¹ increased mineral deposition and upregulated the expression of related osteo/odontogenic markers along with the elevated expression of β-catenin and phosphorylation level of Smad1/5/9. Furthermore, Wnt signaling inhibition using DKK1 and BMP signaling inhibition using noggin inhibited PBM-induced osteo/odontogenic marker expression when used individually or jointly. In conclusion, PBM induces the osteo/odontogenic differentiation of SHEDs through cross talk between BMP/Smad and Wnt/β-catenin signaling pathways.     

Secondary-flow-aided single-train elastic-inertial focusing in low elasticity viscoelastic fluids

Elastic-inertial focusing has attracted increasing interest in recent years due to the three-dimensional (3D) single-train focusing ability it offers. However, multi-train focusing, instead of single-train focusing, was observed in viscoelastic fluids with low elasticity as a result of the competition between inertia effect and viscoelasticity effect. To address this issue, we employed the secondary flow to facilitate single-train elastic-inertial focusing in low elasticity viscoelastic fluids. A three-section contraction-expansion channel was designed to induce the secondary flow to pinch the multiplex focusing trains into a single one exactly at the channel centerline. After demonstrating the focusing process and mechanism in our device, we systematically explored and discussed the effects of particle diameter, operational flow rate, polymer concentration, and channel dimension on particle focusing performances. Our device enables single-train focusing of particles in viscoelastic fluids with low elasticity, and offers advantages of planar single-layer structure, and sheathless, external-field free operation.     

金属氧化物催化剂上合成气转化中羧酸盐物种促进芳烃的生成

芳烃是重要的化工原料,目前主要通过石油催化裂化和催化重整制得.随着石油资源的消耗以及芳烃的需求日益增长,开发非石油路线制备芳烃势在必行.因此,从煤、天然气和生物质出发,经合成气一步制芳烃(STA)广受关注.将合成气制甲醇的金属催化剂和甲醇制芳烃的分子筛催化剂复合,可以制备双功能催化剂,用于合成气反应可高选择性得到芳烃.然而,关于此过程中芳烃的生成机理仍有争论.目前人们认为,生成芳烃的中间体主要分甲醇和其他含氧物种(乙烯酮,醛类)两种.本文以ZnCrAlOx和H-ZSM-5为模型催化剂,进行合成气制芳烃、甲醇制芳烃和丙烯制芳烃反应,确定了传统的甲醇制芳烃路径不是合成气制芳烃中的主要途径,并通过原位傅里叶变换红外光谱和气相色质谱解释了STA反应中两种活性组分距离越近,芳烃选择性越高的原因,从而提出了在合成气制芳烃过程中芳烃的生成机理.通过比较双功能催化剂上合成气、甲醇以及丙烯的反应性能发现,在甲醇和丙烯转化时,其芳烃选择性远小于合成气转化时的,由此可认为,在合成气制芳烃的路径主要不经由传统的甲醇制芳烃,而是通过烯烃聚合脱氢生成芳烃.红外表征和共进料实验表明,合成气可以在金属催化剂表面生成甲酸盐物种,它可与烯烃反应生成羧酸盐物种,再迁移到分子筛上反应生成芳烃,且羧酸盐物种在分子筛上的芳构化能力要高于丙烯;即使在氢气氛围下,当丙烯的芳构化能力受到氢气极大抑制时,羧酸盐物种仍能高选择性生成芳烃.本文制备了一系列金属催化剂和分子筛物理接近距离不同的双功能催化剂,研究了合成气在双功能催化剂上制芳烃时,金属催化剂和分子筛二者组分的距离对芳烃选择性的影响.随着二者接近距离的增加,芳烃选择性急剧增加;通过GC-MS分析合成气转化时的停留物种,发现随着二者接近距离的增加,羧酸盐物种和甲基环戊烯酮的量明显增加,因此,羧酸盐物种和甲基环戊烯酮物种在生成芳烃中起到了重要的作用.综上所述,我们提出了STA中一条新的芳烃生成路径,并证明了羧酸盐物种是其中重要的中间物种.它经由金属表面的甲酸盐物种和烯烃反应生成,随后迁移到分子筛上生成甲基环戊烯酮物种,再脱水生成芳烃.     

Bimetallic CuCo Derived from Prussian Blue Analogue for Nonenzymatic Glucose Sensing

Bimetallic CuCo composites are prepared by calcinating copper hexacyanocobaltate precursor in N₂ atmosphere. The CuCo modified electrodes are fabricated for nonenzymatic glucose sensing in the alkaline electrolyte. The glucose can be directly electro-oxidized on the surface of the electrode catalyst mediated by the redox couples of Cu and Co. The optimal glucose sensor exhibits a high sensitivity (567 μA ⋅ mM⁻¹ ⋅ cm⁻²) in the range up to 825 μM with a detection limit of 3 μM and acceptable selectivity. The sensor can also be applied in serum samples. This work provides a facile and easily-scalable synthesis method of electrocatalysts for nonenzymatic glucose sensors.     

Improving the sensitivity of cellulose fiber-based lateral flow assay by incorporating a water-dissolvable polyvinyl alcohol dam

Cellulose - Lateral flow assay (LFA) is an important point-of-care (POC) test platform due to the associated portability, on-site testing, and low cost for diagnosis of pathogen infections and...