Hensley?s problem for complex and non-Archimedean meromorphic functions

Büchi?s problem asks if there exists a positive integer M such that all x₁,…,xM∈Z satisfying the equations for all 3?r?M must also satisfy for some integer x. Hensley?s problem asks if there exists a positive integer M such that, for any integers ν and a, if ²(ν+r)−a is a square for 1?r?M, then a=0. It is not difficult to see that a positive answer to Hensley?s problem implies a positive answer to Büchi?s problem. One can ask a more general version of the Hensley?s problem by replacing the square by n-th power for any integer n?2 which is called the Hensley?s n-th power problem. In this paper we will solve Hensley?s n-th power problem for complex meromorphic functions and non-Archimedean meromorphic functions.     

Dynamics of species in a model with two predators and one prey

In this paper, we study a predator-prey model which has one prey and two predators with Beddington-DeAngelis functional responses. Firstly, we establish a set of sufficient conditions for the permanence and extinction of species. Secondly, the periodicity of positive solutions is studied. Thirdly, by using Liapunov functions and the continuation theorem in coincidence degree theory, we show the global asymptotic stability of such solutions. Finally, we give some numerical examples to illustrate the behavior of the model.     

HPAI 9G DNAChip: discrimination of highly pathogenic influenza virus genes

The HPAI 9G DNAChip discriminates the single nucleotide polymorphism of H5N1, H5N1 (K), and H5N3 in a 60:1 ratio. It allows the simultaneous detection of highly pathogenic avian influenza viruses with a signal to background ratio of 200 and 100% target-specific hybridization in 30 min at 25 °C.     

Assembly of Three 2D Metal‐Organic Frameworks (MOFs) Derived from Flexible Ligands, 1,4‐bis(3‐pyridyl)‐2,3‐diaza‐1,3‐butadiene (3‐bpd) and/or 1,2‐bis(4‐pyridyl)ethane (dpe)

Three coordination polymers, {[Cd(3‐bpd)₂(NCS)₂]×C₂H₅OH}_n ( 1 ), {[Cd(3‐bpd)(dpe)(NO₃)₂]×(3‐bpd)}₂ ( 2 ), {[Cd(dpe)₂(NCS)₂]×3‐bpd×2H₂O}_n ( 3 ) (3‐bpd = 1,4‐bis(3‐pyridyl)‐2,3‐diaza‐1,3‐butadiene; dpe = 1,2‐bis(4‐pyridyl)ethane), were prepared and structurally characterized by a single‐crystal X‐ray diffraction method. In compound 1 , each Cd(II) ion is six‐coordinate bonded to six nitrogen atoms from four 3‐bpd and two NCS^? ligands. The 3‐bpd acts as a bridging ligand connecting the Cd(II) ion to generate a 2D layered metal‐organic framework (MOF) by using a rhomboidal‐grid as the basic building units with the 4⁴ topology. In compound 2 , the Cd(II) ion is also six‐coordinate bonded to four nitrogen atoms of two 3‐bpd, two dpe and two oxygen atoms of two NO₃^? ligands. The 3‐bpd and dpe ligands both adopt bis‐monodentate coordination mode connecting the Cd(II) ions to generate a 2D layered MOF by using a rectangle‐grid as the basic building units with the 4⁴ topology. In compound 3 , two crystallographically independent Cd(II) ions are both coordinated by four nitrogen atoms of dpe ligands in the basal plane and two nitrogen atom of NCS^? in the axial sites. The dpe acts as a bridging ligand to connect the Cd(II) ions forming a 2D interpenetrating MOFs by using a square‐grid as the basic unit with the 4⁴ topology. All of their 2D layered MOFs in compounds 1 ‐ 3 are then arranged in a parallel non‐interpenetrating ABAB—packing manner in 1 and 2 , and mutually interpenetrating manner in 3 , respectively, to extend their 3D supramolecular architectures with their 1D pores intercalated with solvent (ethanol in 1 or H₂O in 3 ) or free 3‐bpd molecules in 2 and 3 , respectively. The photoluminescence measurements of 1 ‐ 3 reveal that the emission is tentatively assigned to originate from π‐π* transition for 1 and 2 and probably due to ligand‐center luminescence for compounds 3 , respectively.     

High-resolution bone microstructure imaging based on ultrasonic frequency-domain full-waveform inversion

The main challenge in bone ultrasound imaging is the large acoustic impedance contrast and sound velocity differences between the bone and surrounding soft tissue. It is difficult for conventional pulse-echo modalities to give accurate ultrasound images for irregular bone boundaries and microstructures using uniform sound velocity assumption rather than getting a prior knowledge of sound speed. To overcome these limitations, this paper proposed a frequency-domain fullwaveform inversion(FDFWI) algorithm for bone quantitative imaging utilizing ultrasonic computed tomography(USCT).The forward model was calculated in the frequency domain by solving the full-wave equation. The inverse problem was solved iteratively from low to high discrete frequency components via minimizing a cost function between the modeled and measured data. A quasi-Newton method called the limited-memory Broyden–Fletcher–Goldfarb–Shanno algorithm(L-BFGS) was utilized in the optimization process. Then, bone images were obtained based on the estimation of the velocity and density. The performance of the proposed method was verified by numerical examples, from tubular bone phantom to single distal fibula model, and finally with a distal tibia-fibula pair model. Compared with the high-resolution peripheral quantitative computed tomography(HR-p QCT), the proposed FDFWI can also clearly and accurately presented the wavelength scaled pores and trabeculae in bone images. The results proved that the FDFWI is capable of reconstructing high-resolution ultrasound bone images with sub-millimeter resolution. The parametric bone images may have the potential for the diagnosis of bone disease.     

Generalized Büchi’s problem for algebraic functions and meromorphic functions

Büchi’s nth power problem asks is there a positive integer M such that any sequence ${(x_1^n,\ldots ,x_M^n)}$ of nth powers of integers with nth difference equal to n! is necessarily a sequence of nth powers of successive integers. In this paper, we study an analogue of this problem for meromorphic functions and algebraic functions.     

基于弹性模量检测骨疲劳的超声导波方法研究

研究早期诊断骨疲劳的方法是当前骨质评价方面的研究热点之一. 本文对不同弹性模量下长骨中超声导波的传播特性进行了理论分析和仿真研究.首先, 通过数值计算得到导波在管状长骨中的理论解析解.然后对管状长骨进行了时域有限差分(FDTD) 仿真, 并验证了它与理论解析解的一致性, 同时得到长骨中不同模式导波群速度、 中心频率和衰减与弹性模量的关系.研究结果表明各个导波模式的群速度和中心频率均随弹性模量的增加而增加, 而衰减随弹性模量的增加而减小.说明超声导波的传播特性参量可以反映长骨弹性模量的变化, 从而为长骨的早期疲劳诊断提供理论依据.     

欧拉-伯努利梁运动场的正交性及其能量传导特性分析

从无阻尼欧拉—伯努利梁振动方程解析解出发, 推导了有限长梁的关于谱系数的时间—空间平均能量和功率流表达式. 在此基础上, 从泛函分析观点, 探讨了弯曲运动场: 衰减振动、行波模式分解关于能量、功率泛函的正交性. 结果表明: 弯曲衰减振动模式和行波模式关于功率流、机械能时间—空间平均是相互独立的, 即关于场能和场功率互不干涉, 满足叠加原理; 衰减振动场导能与行波场导能的重要区别在于功率流关于右、左衰振动模式分解不满足叠加原理, 即弯曲衰减振动场间的相互"干涉"是使其具有能量传导能力的内在原因. 通过右端集中阻尼器支撑的梁的稳态功率流仿真分析计算, 表明低频区振动导能不可忽略, 同时, 衰减振动场和行波场间存在一定的能量交换现象, 但随着频率升高, 振动场传导能量不断下降, 同时能量传导效率也不断下降.      

Reactor decay heat in 239Pu: solving the γ discrepancy in the 4-3000-s cooling period

The β feeding probability of (102,104,105,106,107)Tc, 105Mo, and 101Nb nuclei, which are important contributors to the decay heat in nuclear reactors, has been measured using the total absorption technique. We have coupled for the first time a total absorption spectrometer to a Penning trap in order to obtain sources of very high isobaric purity. Our results solve a significant part of a long-standing discrepancy in the γ component of the decay heat for 239Pu in the 4-3000 s range.