On generalized perfect difference sets constructed from Sidon sets

Let $\mathbb{N}$ be the set of positive integers. For a nonempty set A of integers and every integer u, denote by $d_A(u)$ the number of $(a,a^{\prime })$ with $a,a^{\prime }\in A$ such that $u=a-a^{\prime }$. For a sequence S of positive integers, let $S(x)$ be the counting function of S. The set $A\subseteq \mathbb{N}$ is called a perfect difference set if $d_A(u)=1$ for every positive integer u. In 2008, Cilleruelo and Nathanson (2008) [4] constructed dense perfect difference sets from dense Sidon sets. In this paper, as a main result, we prove that: let $f:\mathbb{N}\to \mathbb{N}$ be an increasing function satisfying $f(n)\ge 2$ for any positive integer n, then for every Sidon set B and every function $\omega (x)\to \infty$, there exists a set $A\subseteq \mathbb{N}$ such that $d_A(u)=f(u)$ for every positive integer u and $B(x/3)-\omega (x)\le A(x)\le B(x/3)+\omega (x)$ for all $x\ge C_{f,B,\omega }$.     

Sentinel-2卫星的多光谱轻量级船舶目标检测算法

近年来深度卷积神经网络在可见光船舶检测方面取得了显著的进展，然而，大多数相关研究是通过改进大型的网络结构来提高检测性能，因此加大了对更高计算机性能的需求。此外，可见光图像难以在云、雾、海杂波、黑夜等复杂场景检测到船舶。针对以上问题，提出了一种融合红（red, R）、绿（green, G）、蓝（blue, B）和近红外（NIR）4个波段光谱信息的由粗到精细的轻量型船舶检测算法。与现有的方法中根据光谱特性利用水体检测算法提取水体区域不同之处是该算法是利用改进的水体检测算法来提取船舶候选区域。为获取更准确的候选区域，对船舶、厚云、薄云、平静海面、杂波海面5种场景中4个波段的像素值进行了统计分析，选取近红外大于阈值作为辅助判断，并以其中心点获取候选区域32×32大小的切片，并对切片进行非极大值抑制，由此获得了船舶粗检测结果。随后构建了轻量级LSGFNet网络对船舶候选区域切片进行精细识别。构建的网络融合了1×1卷积提取的波谱特征与3×3的提取几何特征，为防止光谱特征与几何特征的信息在融合时“信息不流通”，在LSGFNet网络中引入了ShuffleNet中的通道打乱机制，并减小了模型结构，与典型的轻量级网络相比具有更好的效果且模型较小。最后，利用Sentinel-2卫星多光谱10 m分辨率数据构建了512×512大小的1 120组数据进行粗检测，以及32×32大小的6 014组数据进行精细网络训练，其中候选区域粗提取的查全率为98.99%，精细识别网络精确度为96.04%，不同场景下的平均精确度为92.98%。实验表明该算法在抑制云层、海浪杂波等干扰的复杂背景下具有较高的检测效率，且训练时间短、计算机性能需求低。     

A dried blood spot assay with HPLC–MS/MS for the determination of larotrectinib in mouse blood and its application to a pharmacokinetic study

Larotrectinib is a first-generation tropomyosin kinase inhibitor, approved for the treatment of solid tumors. In this paper, we present a validated dried blood spot (DBS) method for the quantitation of larotrectinib from mouse blood using HPLC–MS/MS, which was operated under multiple reaction monitoring mode. To the DBS disc cards, acidified methanol enriched with internal standard (IS; enasidenib) was added and extracted using tert-butyl methyl ether as an extraction solvent with sonication. Chromatographic separation of larotrectinib and the IS was achieved on an Atlantis dC₁₈ column using 10 mm ammonium formate–acetonitrile (30:70, v/v) delivered at a flow-rate of 0.80 ml/min. Under these optimized conditions, the retention times of larotrectinib and the IS were ~0.93 and 1.37 min, respectively. The total run time was 2.50 min. Larotrectinib and the IS were analyzed using positive ion scan mode and parent–daughter mass to charge ion (m/z) transitions of 429.1 → 342.1 and 474.1 → 267.1, respectively, were used for the quantitation. The calibration range was 1.06–5,080 ng/ml. No matrix effect or carryover was observed. Hematocrit did not influence DBS larotrectinib concentrations. All of the validation parameters met the acceptance criteria. The applicability of the validated method was shown in a mouse pharmacokinetic study.     

Time-dependent Ginzburg–Landau equations for multi-gap superconductors

We numerically solve the time-dependent Ginzburg–Landau equations for two-gap superconductors using the finite-element technique. The real-time simulation shows that at low magnetic field, the vortices in small-size samples tend to form clusters or other disorder structures. When the sample size is large, stripes appear in the pattern. These results are in good agreement with the previous experimental observations of the intriguing anomalous vortex pattern, providing a reliable theoretical basis for the future applications of multi-gap superconductors.     

内插法在相关干涉仪测向体制中的应用

测向误差的减小一直以来都是无线电测向精度提高的一个难点,对于不同的测向体制所采用的减小测向误差的方法都不尽相同。本文主要介绍的是相关干涉仪测向体制的基本原理以及通过内插法的应用来减小测向误差的方法。     

Positive ground state solutions for Schrödinger–Poisson system with critical nonlocal term in ℝ3

This paper is dedicated to studying the following Schrödinger–Poisson system $$\left\{\begin{array}{ll}-\mathrm{\Delta }u+V(x)u-K(x)\varphi |u{|}^{3}u=a(x)f(u),& x\in {ℝ}^3,\\ -\mathrm{\Delta }\varphi =K(x)|u{|}^5,& x\in {ℝ}^3.\end{array}\right.$$ Under some different assumptions on functions V(x), K(x), a(x) and f(u), by using the variational approach, we establish the existence of positive ground state solutions.     

80.5 MeV/u碳离子诱发铜靶的放射性剩余产物测量

高能重带电粒子能直接穿透靶原子核外电子层,与原子核发生直接碰撞,发生散裂反应,产生一系列具有放射性的剩余产物核.重带电粒子诱发靶材放射性剩余核与辐射防护和人员安全有着密切联系,当前,大部分剩余核产额主要依靠蒙特卡罗粒子输运程序进行模拟计算,其准确程度亟需通过实验测量进行准确评估.本文利用能量为80.5 MeV/u的(12)^C⁶⁺粒子对薄铜靶开展了辐照实验与伽玛射线测量,结合伽玛谱学分析方法,得出了辐照产生的18种放射性剩余产物的初始活度和产生截面值,并与PHITS模拟结果进行对比.结果表明,PHITS模拟程序对放射性剩余核种类的估计具有较高可靠性,在其绝对产额方面,与实验测量仍具有较大偏差.     

Potts models with magnetic field: Arithmetic,geometry, and computation

We give a sheaf theoretic interpretation of Potts models with external magnetic field, in terms of constructible sheaves and their Euler characteristics. We show that the polynomial countability question for the hypersurfaces defined by the vanishing of the partition function is affected by changes in the magnetic field: elementary examples suffice to see non-polynomially countable cases that become polynomially countable after a perturbation of the magnetic field. The same recursive formula for the Grothendieck classes, under edge-doubling operations, holds as in the case without magnetic field, but the closed formulae for specific examples like banana graphs differ in the presence of magnetic field. We give examples of computation of the Euler characteristic with compact support, for the set of real zeros, and find a similar exponential growth with the size of the graph. This can be viewed as a measure of topological and algorithmic complexity. We also consider the computational complexity question for evaluations of the polynomial, and show both tractable and NP-hard examples, using dynamic programming.