Further explorations on bridged 1,2,4-trioxanes

Three new bicyclo[3.2.1]-type 1,2,4-trioxanes have been designed and synthesized. One of them demonstrates better tolerance of the intramolecular hemiketals to steric crowding in hydroperoxidation. The other represents a prototype for possible manipulation of the transient radicals generated in cleavage reactions. A new substitution pattern in the bridged system is explored through synthesis of the third molecule. The configurations of all stereogenic centers in the bridged system can be effectively controlled by the chirality of the allyl alcohol as illustrated by the enantioselective synthesis of the fourth molecule. Finally, similar bicyclo[3.3.1]-type 1,2,4-trioxanes are shown very difficult to be synthesized because of the involvement of a conformer with two substituents at axial positions at the same time.     

UNBOUNDED COMPLEX SYMMETRIC TOEPLITZ OPERATORS

In this paper,we study unbounded complex symmetric Toeplitz operators on the Hardy space H²(D) and the Fock space g².The technique used to investigate the complex symmetry of unbounded Toeplitz operators is different from that used to investigate the complex symmetry of bounded Toeplitz operators.     

Construction of Spatiotemporal-Coupling Optimal Low-Dimensional Dynamical Systems for Compressible Navier-Stokes Equations; [可压缩 Navier-Stokes 方程的时空耦合优化低维动力系统建模方法]北大核心CSCD

For the low-dimensional dynamical system model to study dynamics properties of Navier-Stokes equations, it is very important that the attraction domain of the low-dimensional model is the same as that of Navier-Stokes equations. However, to date, there is no universal approach to ensure this purpose for general problems. Herein, it is found that any low-dimensional model based on spatial bases, such as proper orthogonal decomposition bases, optimal spatial bases, and other classical spatial bases, is not predictable, i.e., the error increases with the time evolution of the flow field. With the theoretical framework for building optimal dynamical systems and the new concept of spatiotemporal-coupling spectrum expansion, the low-dimensional model for compressible Navier-Stokes equations was constructed to approximate the numerical solution to large-eddy simulation equations, and the numerical results and novel time evolution of spatiotemporal-coupling bases were given. The entire field error is typically below 10−2%, and the average error at each grid point is below 10−8%. The spatiotemporal-coupling optimal low-dimensional dynamical systems can ensure that the attraction domain of the low-dimensional model is the same as that of Navier-Stokes equations. Therefore, characteristic dynamics properties of spatiotemporal-coupling optimal low-dimensional dynamical systems are the same as those of real flow. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

N叉树上的离散时间量子随机行走

通过离散时间量子随机行走的框架,我们研究了在N叉树上的离散时间量子随机行走,该框架不需要硬币空间,仅仅只需要选择一个除了酉性再无其它限制的演化算子,并且包含了使用再生结构的轨道枚举和z变换.作为结果,我们在封闭形式中计算了在根处的振幅的生成函数.     

Numerical blow-up analysis of the explicit L1-scheme for fractional ordinary differential equations

Numerical Algorithms - This paper deals with the blow-up behavior of numerical solutions to nonlinear fractional ordinary differential equations with a dissipative term. Based on the positivity...     

A Review of Results on Axially Symmetric Navier-Stokes Equations,with Addendum by X. Pan and Q. Zhang

In this paper, we give a brief survey of recent results on axially symmetric Navier-Stokes equations (ASNS) in the following categories: regularity criterion, Liouville property for ancient solutions, decay and vanishing of stationary solutions. Some discussions also touch on the full 3 dimensional equations. Two results, closing of the scaling gap for ASNS and vanishing of homogeneous D solutions in 3 dimensional slabs will be described in more detail.In the addendum, two new results in the 3rd category will also be presented, which are generalizations of recently published results by the author and coauthors.     

Promote Intratumoral Drug Release and Penetration to Counteract Docetaxel-Induced Metastasis by Photosensitizer-Modified Red Blood Cell Membrane-Coated Nanoparticle

The red blood cell membrane (RBCm) provides tight protection, lowers the immunogenicity, and prolongs the circulation time of drugs in vivo when acting as the coating of drug delivery systems. However, the cellular uptake and release of drugs are hindered by RBCm. Docetaxel (DTX) is the first-line medicine for treating triple-negative breast cancer (TNBC), but it induces tumor metastasis. To solve these dilemmas, in this study, the photosensitizer 1,1-dioctadecyl-3,3,3,3-tetramethylindotricarbocyanine iodide (DiR)-modified RBCm (DM) is prepared, which is coated onto a hybrid micelle consisting of the prodrugs of DTX and the anti-metastasis agent calcitriol (CTL), obtaining a nanoparticle, named HDC-DM. In a 4T1 tumor-bearing mouse model, after injecting HDC-DM, the intratumoral DTX and CTL concentrations are increased by 1.7 and 2.5 times compared with the free drug groups. After irradiating tumors with near-infrared laser, DiR elicits the photothermal effect, triggering the rupture of RBCm and drug release, promoting drug penetration in tumors, and inducing immunogenic cell death. The tumor growth inhibition rate is 77%, and the formation of lung metastases is reduced by 82%, with good biocompatibility. It is suggested that the combination of phototherapy, chemotherapy, and anti-metastatic therapy using HDC-DM is expected to be a powerful strategy for treating TNBC.     

Challenges and Opportunities of Implantable Neural Interfaces: From Material,Electrochemical and Biological Perspectives

The desirable implantable neural interfaces can accurately record bioelectrical signals from neurons and regulate neural activities with high spatial/time resolution, facilitating the understanding of neuronal functions and dynamics. However, the electrochemical performance (impedance, charge storage/injection capacity) is limited with the miniaturization and integration of neural electrodes. The “crosstalk” caused by the uneven distribution of elctric field leads to lower electrical stimulation/recording efficiency. The mismatch between stiff electrodes and soft tissues exacerbates the inflammatory responses, thus weakening the transmission of signals. Though remarkable breakthroughs have been made through the incorporation of optimizing electrode design and functionalized nanomaterials, the chronic stability, and long-term activity in vivo of the neural electrodes still need further development. In this review, the neural interface challenges mainly on electrochemistry and biology are discussed, followed by summarizing typical electrode optimization technologies and exploring recent advances in the application of nanomaterials, based on traditional metallic materials, emerging 2D materials, conducting polymer hydrogels, etc., for enhancing neural interfaces. The strategies for improving the durability including enhanced adhesion and minimized inflammatory response, are also summarized. The promising directions are finally presented to provide enlightenment for high-performance neural interfaces in future, which will promote profound progress in neuroscience research.     

Grafted MXenes Based Electrolytes for 5V-Class Solid-State Batteries

Polymer blends based solid polymer electrolytes (SPEs), combining the advantages of multiple polymers, are promising for the utilization of 5 V-class cathodes (e.g., LiCoMnO₄ (LCMO)) with enhanced safety. However, severe macro-phase separation with defects and voids in polymer blends restrict the electrochemical stability and ionic migration of SPEs. Herein, inorganic compatibilizer polyacrylonitrile grafted MXene (MXene-g-PAN) is exploited to improve the miscibility of the poly(vinylidene fluoride-co-hexafluoropropylene) (PVHF)/PAN blends and suppress the consolidation of phase particles. The resulting SPE exhibits a high anodic stability with an ionic conductivity of 2.17 × 10⁻⁴ S cm⁻¹, enabling a stable and reversible Li platting/stripping (over 2500 h). The fabricated solid Li‖LCMO cell delivers a 5.1 V discharge voltage with a decent capacity (131 mAh g⁻¹) and cycling performance. Subsequently, the solid all-in-one graphite‖LCMO battery is also constructed to extend the application of MXene based SPEs in flexible batteries. Benefiting from the interface-less design, outstanding mechanical flexibility and stability is achieved in the battery, which can endure various deformations with a low-capacity loss (< ≈10%). This study signifies a significant development on solid flexible lithium ion batteries with enhanced performance, stability, and reliability by investigating the miscibility of polymer blends, benefiting for the design of high-performance SPEs.