Differentiable spaces that are subcartesian

We show that the differential structure of the orbit space of a proper action of a Lie group on a smooth manifold is weakly reflexive. This implies that the orbit space is a differentiable space in the sense of Smith, which ensures that the orbit space has an exterior algebra of differential forms, that satisfies Smith’s version of de Rham’s theorem. Because the orbit space is a locally closed subcartesian space, it has vector fields and their flows.     

Superswelling Microneedle Arrays for Dermal Interstitial Fluid (Prote)Omics

The noninvasive sampling of dermal interstitial fluid (ISF) for the monitoring of clinical biomarkers is a greatly appealing area of research. The identification of molecular biomarkers in biological fluids has been accelerated with -omics analyses but remains limited in ISF because of its time-consuming and complex extraction process. Here, the generation of microneedle (MN) patches made of superabsorbent acrylate-based hydrogels for the rapid sampling of dermal ISF is described to explore its proteome. In depth, iterative optimization allows the identification of novel acrylate-based compositions with the required chemical, mechanical, and biocompatibility properties allowing proteomic analysis of the extracted ISF for the first time after sampling with swelling MNs. The generated MN arrays show no cytotoxic effect, successfully cross the stratum corneum, and can collect up to 6 µL of dermal ISF in 10 min in vivo. Proteomics lead to the detection of 176 clinically relevant biomarkers in the collected samples validating the use of ISF as a relevant bodily fluid for disease monitoring and diagnostic. Importantly, it is discovered that extraction fingerprint is strongly dependent on the MNs chemistry, and thus specific biomarkers could be selectively extracted by tuning the composition of the patch, making the system versatile and specific.     

The full basis theorem does not imply analytic wellordering

A finite support product of ${\omega }_1$ clones of Jensen's minimal ${\Pi }_2^1$ singleton forcing is used to define a model in which any non-empty analytically definable set of reals contains an analytically definable real (the full basis theorem), but there is no analytically definable wellordering of the reals.     

Liouville theorem for weighted p-Lichnerowicz equation on smooth metric measure space

In this paper, let $(M^n,g,d\mu )$ be n-dimensional noncompact metric measure space which satisfies Poincaré inequality with some Ricci curvature condition. We obtain a Liouville theorem for positive weak solutions to weighted p-Lichnerowicz equation

${△}_{p,f}v+c{v}^{\sigma }=0,$

where $c\le 0,m>n\ge 1,1<p<\frac{m?1+\sqrt{(m?1)(m+3)}}{2},\sigma \le p?1$ are real constants.     

Boundedness of semilinear Duffing equations at resonance in a critical situation

In this paper, we propose a sufficient and necessary condition for the boundedness of all the solutions for the equation $\ddot{x}+n^{2}x+g(x)=p(t)$ with the critical situation that $|{\int }_0^{2\pi }p(t)e^{?int}dt|=2|g(+\infty )?g(?\infty )|$ on g and p, where $n\in {\mathbb{N}}^{+}$, $p(t)$ is periodic and $g(x)$ is bounded.     

Current air quality analytics and monitoring: A review

This review summarizes the different tools and concepts that are commonly applied in air quality monitoring. The monitoring of atmosphere is extremely important as the air quality is an important problem for large communities. Main requirements for analytical devices used for monitoring include a long period of autonomic operation and portability. These instruments, however, are often characterized by poor analytical performance. Monitoring networks are the most common tools used for monitoring, so large-scale monitoring programmes are summarized here. Biomonitoring, as a cheap and convenient alternative to traditional sample collection, is becoming more and more popular, although its main drawback is the lack of standard procedures. Telemonitoring is another approach to air monitoring, which offers some interesting opportunities, such as ease of coverage of large or remote areas, constituting a complementary approach to traditional strategies; however, it requires huge costs.     

传感器管理及其在相控阵雷达中的应用

传感器管理是数据融合的一部分。介绍了传感器管理的概念和框架 ,概述了国内外传感器管理算法的研究现状。主要工作是针对相控阵雷达这一传感器 ,通过对其不同工作模式以及不同参数的管理 ,来说明传感器管理的原理。提出了一种新的自适应采样周期算法 ,仿真结果表明该算法的优越性