Nonlinear elastic constitutive relations of residually stressed composites with stiff curved fibres

Applied Mathematics and Mechanics - Mechanical models of residually stressed fibre-reinforced solids, which do not resist bending, have been developed in the literature. However, in some residually...     

Existential monadic second order logic of undirected graphs: The Le Bars conjecture is false

In 2001, J.-M. Le Bars disproved the zero-one law (that says that every sentence from a certain logic is either true asymptotically almost surely (a.a.s.), or false a.a.s.) for existential monadic second order sentences (EMSO) on undirected graphs. He proved that there exists an EMSO sentence ? such that $\mathsf{P}(G_n??)$ does not converge as $n\to \infty$ (here, the probability distribution is uniform over the set of all graphs on the labeled set of vertices $\{1,\dots ,n\}$). In the same paper, he conjectured that, for EMSO sentences with 2 first order variables, the zero-one law holds. In this paper, we disprove this conjecture.     

Non‐self‐adjoint singular second‐order dynamic operators on time scale

In this study, maximal dissipative second‐order dynamic operators on semi‐infinite time scale are studied in the Hilbert space , that the extensions of a minimal symmetric operator in limit‐point case. We construct a self‐adjoint dilation of the dissipative operator together with its incoming and outgoing spectral representations so that we can determine the scattering function of the dilation as stated in the scheme of Lax‐Phillips. Moreover, we construct a functional model of the dissipative operator and identify its characteristic function in terms of the Weyl‐Titchmarsh function of a self‐adjoint second‐order dynamic operator. Finally, we prove the theorems on completeness of the system of root functions of the dissipative and accumulative dynamic operators.     

On concentration of solution to a Schrödinger logarithmic equation with deepening potential well

In this work, we prove the existence of positive solution for the following class of problems where λ>0 and is a potential satisfying some conditions. Using the variational method developed by Szulkin for functionals, which are the sum of a C¹ functional with a convex lower semicontinuous functional, we prove that for each large enough λ>0, there exists a positive solution for the problem, and that, as λ→+∞, such solutions converge to a positive solution of the limit problem defined on the domain Ω=int(V^?1({0})).     

d-Orbital Reconstructions Forced by Double Bow-Shaped Deformations and Second Coordination Sphere Effects of Cu(II) Heme Analogs in HER**

Both geometric architecture and electronic configurations of heme proteins contribute to its activity. In this work we designed and synthesized a series of four copper(II) porphyrin complexes ( 4 -, 3 -, 2 - and 1 -Cu) where the molecular conformations are modulated by a pair of stepwise shortened straps on the same porphyrin side (cis-ortho) to give double bow-shaped skeletons. Single crystal structures demonstrate that the straps gradually increase the saddle deformation and the deviation of the metal centers, which is in accordance with two, unusual d-orbital reconstructions of two different ground states, as revealed by 4 K EPR and DFT calculations. In the study of the electrocatalytic hydrogen evolution reaction (HER), 1 -Cu, with the shortest straps, showed the most apparent improvement of activity. Second coordination sphere (SCS) effects created by the double bow-shaped architecture and the strong saddle porphyrin core in 1 -Cu are found to play key roles in proton trapping during the catalytic process. The work contributes a novel strategy to improve the catalytic performance of heme analogs through ligand geometric modulation.     

一类正交空间填充设计的构造

空间填充设计在计算机试验中应用十分广泛,当拟合回归模型时,正交的空间填充设计保证了因子效应估计的独立性.基于广义正交设计,文章给出了构造二阶正交拉丁超立方体设计和列正交设计的方法,新构造的设计不仅满足任意两列之间相互正交,还能保证每一列与任一列元素平方组成的列以及任两列元素相乘组成的列都正交.当某些正交的空间填充设计不存在时,具有较小相关系数的近似正交设计可作为替代设计使用.设计构造的灵活性为计算机试验在实践中的广泛应用提供了必要的支持.     

Li[LiCs2Cl][Ga3S6]: A Nanoporous Framework of GaS4 Tetrahedra with Excellent Nonlinear Optical Performance

A large nonlinear optical (NLO) coefficient and a wide band gap are two crucial but contradictory parameters that are difficult to achieve simultaneously in a single infrared (IR) NLO compound. A salt‐inclusion chalcogenide (SIC), Li[LiCs₂Cl][Ga₃S₆] ( 1 ), was prepared that presents a nanosized tunnel framework constructed from monotype chalcogenide tetrahedra. Highly oriented covalent GaS₄ tetrahedra in the host lead to a moderate second harmonic generation response (0.7 AgGaS₂), and ionic guests effectively broaden the band gap to the widest value (4.18 eV) among all IR NLO chalcogenides, thereby achieving a remarkable balance between NLO efficiency and band gap.     

Second harmonic magnetoacoustic responses of magnetic nanoparticles in magnetoacoustic tomography with magnetic induction

Due to the unique magnetic, mechanical and thermal properties, magnetic nanoparticles(MNPs) have comprehensive applications as the contrast and therapeutic agents in biomedical imaging and magnetic hyperthermia. The linear and nonlinear magnetoacoustic responses determined by the magnetic properties of MNPs have attracted more and more attention in biomedical engineering. By considering the relaxation time of MNPs, we derive the formulae of second harmonic magnetoacoustic responses(2H-MARs) for a cylindrical MNP solution model based on the mechanical oscillations of MNPs in magnetoacoustic tomography with magnetic induction(MAT-MI). It is proved that only the second harmonic magnetoacoustic oscillations can be generated by MNPs under an alternating magnetic excitation. The acoustic pressure of the 2H-MAR is proportional to the square of the magnetic field intensity and exhibits a linear increase with the concentration of MNPs. Numerical simulations of the 2H-MAR are confirmed by the experimental measurements for various magnetic field intensities and solution concentrations using a laser vibrometer. The favorable results demonstrate the feasibility of the harmonic measurements without the fundamental interference of the electromagnetic excitation, and suggest a new harmonic imaging strategy of MAT-MI for MNPs with enhanced spatial resolution and improved signal-to-noise ratio in biomedical applications.     

扩展基于AD9874数字接收机谱宽的二次抽取算法

针对基于AD9874芯片的数字接收机的最小谱宽和谱宽允许设置的数目均不能满足常规临床用磁共振成像技术的要求,本文从软件角度提出了一种扩展数字接收机谱宽的二次抽取算法. 该算法具体实现过程主要包括两个步骤：(1) 自适应过采样倍率和自动谱宽调整;(2) 数字滤波和抽取. 为了验证这个二次抽取算法的有效性,本文分别用单脉冲实验和磁共振成像实验加以了验证.