Plasmonic Hotspots in Air: An Omnidirectional Three‐Dimensional Platform for Stand‐Off In‐Air SERS Sensing of Airborne Species

Molecular‐level airborne sensing is critical for early prevention of disasters, diseases, and terrorism. Currently, most 2D surface‐enhanced Raman spectroscopy (SERS) substrates used for air sensing have only one functional surface and exhibit poor SERS‐active depth. “Aerosolized plasmonic colloidosomes” (APCs) are introduced as airborne plasmonic hotspots for direct in‐air SERS measurements. APCs function as a macroscale 3D and omnidirectional plasmonic cloud that receives laser irradiation and emits signals in all directions. Importantly, it brings about an effective plasmonic hotspot in a length scale of approximately 2.3 cm, which affords 100‐fold higher tolerance to laser misalignment along the z‐axis compared with 2D SERS substrates. APCs exhibit an extraordinary omnidirectional property and demonstrate consistent SERS performance that is independent of the laser and analyte introductory pathway. Furthermore, the first in‐air SERS detection is demonstrated in stand‐off conditions at a distance of 200 cm, highlighting the applicability of 3D omnidirectional plasmonic clouds for remote airborne sensing in threatening or inaccessible areas.     

A portable microreactor with minimal accessories for polymerase chain reaction: application to the determination of foodborne pathogens

The authors describe a microreactor for performing a multiplexed polymerase chain reaction (PCR) which is operated with minimal accessories such as a single heater for gene amplification and a hand-held syringe for sample actuation. It was fabricated by wrapping a polytetrafluoroethylene (PTFE) tube around a rectangular poly(dimethylsiloxane) (PDMS) block having a predetermined thickness. The resulting portable microreactor was applied to PCR using a single heater because the rectangular PDMS block spatially segregated the upper and lower arrays of the PTFE tube. This warrants the adjustment of distinct temperatures inside the upper and lower tubes. A hand-held plastic syringe was connected to the inlet of the PTFE tube and used as a portable pump to achieve a homogeneous transport of a sample liquid inside the microreactor. The use of gas-impermeable PTFE prevents the formation of bubbles during thermal cycling. The microreactor was successfully applied to the amplification of typical DNA fragments of three foodborne pathogens in less than 30 min. In our perception, this method paves the way to the construction of a truly portable PCR chip that is applicable to rapid clinical diagnosis and the detection of foodborne pathogens.

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Necessary and Sufficient Conditions for Qualitative Properties of Infinite Dimensional Linear Programming Problems

Necessary and sufficient conditions for qualitative properties of infinite dimensional linear programing problems such as solvability, duality, and complementary slackness conditions are studied in this article. As illustrations for the results, we investigate the parametric version of Gale’s example.     

Dynamic Picone's identity and its applications

We prove some Picone-type identities and inequalities for a class of first-order nonlinear dynamic systems and derive various weighted inequalities of Wirtinger type and Hardy type on time scales. As applications we study oscillatory and related properties of these systems including Reid's roundabout theorem on disconjugacy, Sturm's separation and comparison theorems, as well as a variational method in the oscillation theory.     

K3 et formules de Riemann-Hurwitzp-adiques

The well-known formula of Riemann-Hurwitz gives the change of genuses in ann-fold covering of compact connected Riemann surfaces. In Iwasawa theory, there existp-adic analogues which give the change of certain ^±-invariants in ap-extension ofCM number fields. Using functorial and arithmetical properties ofK ₃, we extend such Riemann-Hurwitzp-adic formulas to non-CM fields, assuming some restrictive hypotheses on the capitulation ofK ₂.

     

Finite‐size corrections at the hard edge for the Laguerre β ensemble

A fundamental question in random matrix theory is to quantify the optimal rate of convergence to universal laws. We take up this problem for the Laguerre β ensemble, characterized by the Dyson parameter β, and the Laguerre weight , in the hard edge limit. The latter relates to the eigenvalues in the vicinity of the origin in the scaled variable . Previous work has established the corresponding functional form of various statistical quantities—for example, the distribution of the smallest eigenvalue, provided that . We show, using the theory of multidimensional hypergeometric functions based on Jack polynomials, that with the modified hard edge scaling , the rate of convergence to the limiting distribution is , which is optimal. In the case , general the explicit functional form of the distribution of the smallest eigenvalue at this order can be computed, as it can for and general . An iterative scheme is presented to numerically approximate the functional form for general .     

Dynamically consistent discrete metapopulation model

In this paper we construct nonstandard difference schemes, which are dynamically consistent with a metapopulation model formulated by Keymer et al. in 2000, i.e. preserve all dynamical properties of the differential equations of the model. These properties are: monotone convergence, boundedness, local asymptotic stability and especially, global stability of equilibria and non-periodicity of solutions. Numerical examples confirm the obtained theoretical results of the properties of the constructed difference schemes.