线性模型中广义最小二乘参数估计误差分布的稳健性研究

研究了线性模型中广义最小二乘参数估计的误差分布稳健性问题.首先讨论了在线性统计模型里,设计矩阵为列降秩矩阵时,模型中给出了误差最大分布类,当误差向量的分布在此范围内变动时,LS估计和GLS估计在均方误差矩阵准则下是最优估计.然后进一步探讨广义最小二乘估计GLSE关于误差分布的稳健性,求出误差项所对应的最大分布族,进而证明了在该区间波动情况下,误差向量对应的始终为一致最优解.     

Difference operators for partitions under the Littlewood decomposition

Let n be a positive integer. Let \(\delta _3(n)\) denote the difference between the number of (positive) divisors of n congruent to 1 modulo 3 and the number of those congruent to 2 modulo 3. In 2004, Farkas proved that the arithmetic convolution sum

$$\begin{aligned} D_3(n):=\sum _{j=1}^{n-1}\delta _3(j)\delta _3(n-j) \end{aligned}$$

satisfies the relation

$$\begin{aligned} 3D_3(n)+\delta _3(n)={\sum _{\mathop {_{d \mid n}}\limits _{3 \not \mid d}}}d. \end{aligned}$$

In this paper, we use a result about binary quadratic forms to prove a general arithmetic convolution identity which contains Farkas’ formula and two other similar known formulas as special cases. From our identity, we deduce a number of analogous new convolution formulas.

     

Even factors with a bounded number of components in iterated line graphs

We consider even factors with a bounded number of components in the n-times iterated line graphs L ⁿ (G). We present a characterization of a simple graph G such that L ⁿ (G) has an even factor with at most k components, based on the existence of a certain type of subgraphs in G. Moreover, we use this result to give some upper bounds for the minimum number of components of even factors in L ⁿ (G) and also show that the minimum number of components of even factors in L ⁿ (G) is stable under the closure operation on a claw-free graph G, which extends some known results. Our results show that it seems to be NP-hard to determine the minimum number of components of even factors of iterated line graphs. We also propose some problems for further research.     

Electrochromic Detection of Latent Fingermarks on Metal Surface Using 1,1′-Dibenzyl-4,4′-bipyridinium Dichloride

The electrochromic detection of latent fingermarks on polished or unpolished, flat or curved metal surfaces is described using electrochromic material, 1,1’-dibenzyl-4,4’-bipyridinium dichloride. The surface area covered by fingermarks acts as an insulating mask, causing 1,1’-dibenzyl-4,4’-bipyridinium dichloride to change color and produce inversed images of the fingermark. By changing the applied potential, the optical properties of 1,1’-dibenzyl-4,4’-bipyridinium dichloride can be continuously and reversibly adjusted to optimize the visual contrast of fingermarks, so as to realize the detection of latent fingermarks on stainless steel surface. It is demonstrated that the fabricated electrochromic devices can detect the fingermarks on these types of surfaces within twenty seconds at −1.0∼−2.0 V. This work can qualify as a tangible improvement in fingermark detection of the natural fingermarks on the never-cleaned (more than 3 years) and curved surfaces of daily-used container, e. g. cup, and the handle of cleaning tool, mop.     

A Tailored Versatile and Efficient NHC-Based NNC-Pincer Manganese Catalyst for Hydrogenation of Polar Unsaturated Compounds

The reactivity of metal-hydride complexes can be harnessed by the modification of ancillary ligands. With the aim of improving the hydride-donor ability of the key Mn−H intermediate and reducing steric hindrance, we herein report the rational design of a versatile and efficient NHC-based NNC-pincer Mn catalyst for hydrogenation reactions. This newly developed catalyst exhibited higher activity than the corresponding NNP-pincer Mn catalyst owing to its reduced steric hindrance and enhanced Mn−H σ-bonding orbital energy level through a π-antibonding interaction. Using this highly active NNC-pincer Mn catalyst, a rich array of polar unsaturated compounds (>80 examples) including esters, N-heteroarenes, amides, carbonates, and urea derivatives, were successfully hydrogenated under relatively mild conditions. This work represents a rare example of a general phosphine-free Mn-catalyzed hydrogenation system.     

Precise Epitope Organization with Self-adjuvant Framework Nucleic Acid for Efficient COVID-19 Peptide Vaccine Construction

Peptide vaccines have advantages in easy fabrication and high safety, but their effectiveness is hampered by the poor immunogenicity of the epitopes themselves. Herein, we constructed a series of framework nucleic acids (FNAs) with regulated rigidity and size to precisely organize epitopes in order to reveal the influence of epitope spacing and carrier rigidity on the efficiency of peptide vaccines. We found that assembling epitopes on rigid tetrahedral FNAs (tFNAs) with the appropriate size could efficiently enhance their immunogenicity. Further, by integrating epitopes from SARS-CoV-2 on preferred tFNAs, we constructed a COVID-19 peptide vaccine which could induce high titers of IgG against the receptor binding domain (RBD) of SARS-CoV-2 spike protein and increase the ratio of memory B and T cells in mice. Considering the good biocompatibility of tFNAs, our research provides a new idea for developing efficient peptide vaccines against viruses and possibly other diseases.     

Boosting the Efficiency of Dye-Sensitized Solar Cells by a Multifunctional Composite Photoanode to 14.13 %

We report a new strategy to fabricate a multifunctional composite photoanode containing TiO₂ hollow spheres (TiO₂-HSs), Au nanoparticles (AuNPs) and novel NaYF₄ : Yb,Er@NaLuF₄ : Eu@SiO₂ upconversion nanoparticles (UCNPs). The AuNPs are grown on the photoanode film including TiO₂-HSs and UCNPs by a simple in situ plasmonic treatment. As a result, an impressive power conversion efficiency of 14.13 % is obtained, which is a record for N719 dye-based dye-sensitized solar cells, demonstrating great potential for the solar cells toward commercialization. This obvious enhancement is ascribed to a collaborative mechanism of the TiO₂-HSs exhibiting excellent light-scattering ability, of the UCNPs converting near-infrared photons into visible photons and of the AuNPs presenting outstanding surface plasmon resonance effect. Notably, a steady-state experiment further reveals that the champion cell exhibits 95.33 % retainment in efficiency even after 180 h of measurements, showing good device stability.     

Synthesis of a Porous [14]Annulene Graphene Nanoribbon and a Porous [30]Annulene Graphene Nanosheet on Metal Surfaces

The electrical and mechanical properties of graphene-based materials can be tuned by the introduction of nanopores, which are sensitively related to the size, morphology, density, and location of nanopores. The synthesis of low-dimensional graphene nanostructures containing well-defined nonplanar nanopores has been challenging due to the intrinsic steric hindrance. Herein, we report the selective synthesis of one-dimensional (1D) graphene nanoribbons (GNRs) containing periodic nonplanar [14]annulene pores on Ag(111) and two-dimensional (2D) porous graphene nanosheet containing periodic nonplanar [30]annulene pores on Au(111), starting from a same precursor. The formation of distinct products on the two substrates originates from the different thermodynamics and kinetics of coupling reactions. The reaction mechanisms were confirmed by a series of control experiments, and the appropriate thermodynamic and kinetic parameters for optimizing the reaction pathways were proposed. In addition, the combined scanning tunneling spectroscopy (STS) and density functional theory (DFT) calculations revealed the electronic structures of porous graphene structures, demonstrating the impact of nonplanar pores on the π-conjugation of molecules.     

Multiple Dynamic Bonds-Driven Integrated Cathode/Polymer Electrolyte for Stable All-Solid-State Lithium Metal Batteries

All-solid-state lithium metal batteries (LMBs) are considered as the promising higher-energy and improved-safety energy-storage systems. Nevertheless, the electrolyte-electrodes interfacial issues due to the limited solid physical contact lead to discontinuous interfacial charge transport and large interfacial resistance, thereby suffering from unsatisfactory electrochemical performance. Herein, we construct an integrated cathode/polymer electrolyte for all-solid-state LMBs under the action of polymer chains exchange and recombination originating from multiple dynamic bonds in our well-designed dynamic supramolecular ionic conductive elastomers (DSICE) molecular structure. The DSICE acts as polymer electrolytes with excellent electrochemical performance and mechanical properties, achieving the ultrathin pure polymer electrolyte thickness (12 μm). Notably, the DSICE also functions as lithium iron phosphate (LiFePO₄, LFP) cathode binders with enhanced adhesive capability. Such well-constructed Li|DSICE|LFP-DSICE cells generate delicate electrolyte-electrodes interfacial contact at the molecular level, providing continuous Li⁺ transport pathways and promoting uniform Li⁺ deposition, further delivering superior long-term charge/discharge stability (>600 cycles, Coulombic efficiency, >99.8 %) and high capacity retention (80 % after 400 cycles). More practically, the Li|DSICE|LFP-DSICE pouch cells show stable electrochemical performance, excellent flexibility and safety under abusive tests.