Some birationality criteria on 3-folds with p_g>1 Dedicated to the memory of Professor XIAO Gang

We give some birationality criteria for m(m = 4,5,6,7) on general type 3-folds with pg 2 by means of an intensive classification. In particular,we show that 7 is not birational if and only if pg(X) = 2and X admits a genus 2 curve family of canonical degree23. When the canonical volume is large,we also characterize the birationality of 4,5 and 6.     

Solutions of a second-order Hamiltonian system with periodic boundary conditions

By using the least action principle and the saddle point theorem, some existence theorems are obtained, viz. the existence of solutions to a second-order Hamiltonian system with periodic boundary conditions in the cases when the gradient of the nonlinearity is bounded sublinearly and linearly respectively.     

A semismooth Newton method for nonlinear symmetric cone programming

In this paper, we employ the projection operator to design a semismooth Newton algorithm for solving nonlinear symmetric cone programming (NSCP). The algorithm is computable from theoretical standpoint and is proved to be locally quadratically convergent without assuming strict complementarity of the solution to NSCP.     

Equivalent Conditions for Local Error Bounds

In this paper we present two classes of equivalent conditions for local error bounds in finite dimensional spaces. We formulate conditions of the first class by using subderivatives, subdifferentials and strong slopes for nearby points outside the referenced set, and show that these conditions actually characterize a uniform version of the local error bound property. We demonstrate this uniformity for the max function of a finite collection of smooth functions, and as a consequence we show that quasinormality constraint qualifications guarantee the existence of local error bounds. We further present the second class of equivalent conditions for local error bounds by using the various limits defined on the boundary of the referenced set. In presenting these conditions, we exploit the variational geometry of the referenced set in a systematic way and unify some existing results in the literature.     

Catalytic DNA-Assisted Mass Production of Arbitrary Single-Stranded DNA

Synthetic single-stranded (ss) DNA is a cornerstone for life and materials science, yet the purity, quantity, length, and customizability of synthetic DNA are still limiting in various applications. Here, we present PECAN, p aired-e nd c utting a ssisted by DN Azymes (DNA enzymes or deoxyribozymes), which enables mass production of ssDNA of arbitrary sequence (up to 7000 nucleotides, or nt) with single-base precision. At the core of PECAN technique are two newly identified classes of DNAzymes, each robustly self-hydrolyzing with minimal sequence requirement up- or down-stream of its cleavage site. Flanking the target ssDNA with a pair of such DNAzymes generates a precursor ssDNA amplifiable by pseudogene-recombinant bacteriophage, which subsequently releases the target ssDNA in large quantities after efficient auto-processing. PECAN produces ssDNA of virtually any terminal bases and compositions with >98.5 % purity at the milligram-to-gram scale. We demonstrate the feasibility of using PECAN ssDNA for RNA in situ detection, homology-directed genome editing, and DNA-based data storage.     

A Space-Confined Polymerization Templated by Ice Enables Large-Scale Synthesis of Two-Dimensional Polymer Sheets

Despite significant progress in the preparation and characterization of two-dimensional (2D) materials, the synthesis of 2D organic materials remains challenging. Here, we report a novel space-confined polymerization method that enables the large-scale synthesis of 2D sheets of a functional conjugated polymer, namely, poly(3,4-ethylenedioxythiophene) (PEDOT). A key step in this method is the confinement of monomer to the boundaries of ice crystals using micelles. This spatial confinement directs the polymerization to form 2D PEDOT sheets with high crystallinity and controlled morphology. Supercapacitors prepared from the 2D PEDOT sheets exhibit outstanding performance metrics. In aqueous electrolyte, a high areal specific capacitance of 898 mF cm⁻² at 0.2 mA cm⁻² along with an excellent rate capability is achieved (e.g., capacitance retention of 67.6 % at a 50-fold higher current). Moreover, the 2D PEDOT-based supercapacitors exhibit outstanding cycling stability (capacitance retention of 98.5 % after 30,000 cycles). Device performance is further improved when an organic electrolyte is used.     

Unraveling the Oxidation Behaviors of MXenes in Aqueous Systems by Active-Learning-Potential Molecular-Dynamics Simulation

MXenes are 2D materials with great potential in various applications. However, the degradation of MXenes in humid environments has become a main obstacle in their practical use. Here we combine deep neural networks and an active learning scheme to develop a neural network potential (NNP) for aqueous MXene systems with ab initio precision but low cost. The oxidation behaviors of super large aqueous MXene systems are investigated systematically at nanosecond timescales for the first time. The oxidation process of MXenes is clearly displayed at the atomic level. Free protons and oxides greatly inhibit subsequent oxidation reactions, leading to the degree of oxidation of MXenes to exponentially decay with time, which is consistent with the oxidation rate of MXenes measured experimentally. Importantly, this computational study represents the first exploration of the kinetic process of oxidation of super-sized aqueous MXene systems. It opens a promising avenue for the future development of effective protection strategies aimed at controlling the stability of MXenes.     

Synergetic Coupling of Redox-Active Sites on Organic Electrode Material for Robust and High-Performance Sodium-Ion Storage

Organic electrode materials (OEMs), valued for their sustainability and structural tunability, have been attracting increasing attention for wide application in sodium-ion batteries (SIBs) and other rechargeable batteries. However, most OEMs are plagued with insufficient specific capacity or poor cycling stability. Therefore, it′s imperative to enhance their specific capacity and cycling stability through molecular design. Herein, we designed and synthesized a heteroaromatic molecule 2,3,8,9,14,15-hexanol hexaazatrinaphthalene (HATN-6OH) by the synergetic coupling of catechol (the precursor of ortho-quinone)/ortho-quinone functional groups and HATN conjugated core structures. The abundance of catechol/ortho-quinone and imine redox-active moieties delivers a high specific capacity of nine-electron transfer for SIBs. Most notably, the π–π interactions and intermolecular hydrogen bond forces among HATN-6OH molecules secure the stable long-term cycling performance of SIBs. Consequently, the as-prepared HATN-6OH electrode exhibited a high specific capacity (554 mAh g⁻¹ at 0.1 A g⁻¹), excellent rate capability (202 mAh g⁻¹ at 10 A g⁻¹), and stable long-term cycling performance (73 % after 3000 cycles at 10 A g⁻¹) in SIBs. Additionally, the nine-electron transfer mechanism is confirmed by systematic density functional theory (DFT) calculation, attenuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR), and Raman analysis. The achievement of the synergetic coupling of the redox-active sites on OEMs could be an important key to the enhancement of SIBs and other metal-ion batteries.