Maskless Preparation of Spatially-Resolved Plasmonic Nanoparticles on Polydimethylsiloxane via In Situ Fluoride-Assisted Synthesis

Here, a fluoride-assisted route for the controlled in-situ synthesis of metal nanoparticles (NPs) (i.e., AgNPs, AuNPs) on polydimethylsiloxane (PDMS) is reported. The size and coverage of the NPs on the PDMS surface are modulated with time and over space during the synthetic process, leveraging the improved yield (10×) and faster kinetics (100×) of NP formation in the presence of F⁻ ions, compared to fluoride-free approaches. This enables the maskless preparation of both linear and step gradients and patterns of NPs in 1D and 2D on the PDMS surface. As an application in flexible plasmonics/photonics, continuous and step-wise spatial modulations of the plasmonic features of PDMS slabs with 1D and 2D AgNP gradients on the surface are demonstrated. An excellent spatially resolved tuning of key optical parameters, namely, optical density from zero to 5 and extinction ratio up to 100 dB, is achieved with AgNP gradients prepared in AgF solution for 12 minutes; the performance are comparable to those of commercial dielectric/interference filters. When used as a rejection filter in optical fluorescence microscopy, the AgNP-PDMS slabs are able to reject the excitation laser at 405 nm and retain the green fluorescence of microbeads (100 µm) used as test cases.     

Quantum curves and q-deformed Painlevé equations

Letters in Mathematical Physics - We propose that the grand canonical topological string partition functions satisfy finite-difference equations in the closed string moduli. In the case of genus...     

Sufficient Conditions for a Digraph to be Supereulerian

A (di)graph is supereulerian if it contains a spanning eulerian sub(di)graph. This property is a relaxation of hamiltonicity. Inspired by this analogy with hamiltonian cycles and by similar results in supereulerian graph theory, we analyze a number of sufficient Ore type conditions for a digraph to be supereulerian. Furthermore, we study the following conjecture due to Thomassé and the first author: if the arc‐connectivity of a digraph is not smaller than its independence number, then the digraph is supereulerian. As a support for this conjecture we prove it for digraphs that are semicomplete multipartite or quasitransitive and verify the analogous statement for undirected graphs.     

Near‐Infrared (NIR) Organic Light‐Emitting Diodes (OLEDs): Challenges and Opportunities

The rapid development of the science and technology of organic semiconductors has already led to mass application of organic light‐emitting diodes (OLEDs) in television monitors of outstanding quality as well as in a large variety of smaller displays found in smartphones, tablets, and other gadgets, while introduction of the technology to the illumination sector is imminent. Notably, the requirements of all such applications for emission in the visible range of the electromagnetic spectrum are well tuned to the optical and electronic properties of typical organic semiconductors, thereby representing relatively “low‐hanging fruits,” in terms of material development and exploitation. However, the question arises as to whether developing materials suited for efficient near‐infrared (NIR, 700–1000 nm) emission is possible, and, crucially, desirable to enable new classes of applications spanning from through‐space, short‐range communications to biomedical sensors, night vision, and more generally security applications to name but a few. Here, the major fundamental hurdles to be overcome to achieve efficient NIR emission from organic π‐conjugated systems are discussed, recent progress is reviewed, and an outlook for further development of both materials and applications is provided.     

Two-dimensional vortex sheets for the nonisentropic Euler equations: Nonlinear stability

We show the short-time existence and nonlinear stability of vortex sheets for the nonisentropic compressible Euler equations in two spatial dimensions, based on the weakly linear stability result of Morando and Trebeschi (2008) [20]. The missing normal derivatives are compensated through the equations of the linearized vorticity and entropy when deriving higher-order energy estimates. The proof of the resolution for this nonlinear problem follows from certain a priori tame estimates on the effective linear problem in the usual Sobolev spaces and a suitable Nash–Moser iteration scheme.     

Spectroscopic characterization of core and shell regions in monolayer protected gold nanoparticles

We report studies on the structure of the metallic core and the alkyl cap layer in monolayer protected gold nanoparticles having sizes down to 1.6 nm. These particles are obtained by laser ablating gold targets in alkane-thiol solutions at different concentrations. The electronic structure of gold core and the vibrational properties of the capping hydrocarbon chains reveal effects connected with the nanosized nature of the particles.     

Building kernels from binary strings for image matching.

In the statistical learning framework, the use of appropriate kernels may be the key for substantial improvement in solving a given problem. In essence, a kernel is a similarity measure between input points satisfying some mathematical requirements and possibly capturing the domain knowledge. In this paper, we focus on kernels for images: we represent the image information content with binary strings and discuss various bitwise manipulations obtained using logical operators and convolution with nonbinary stencils. In the theoretical contribution of our work, we show that histogram intersection is a Mercer's kernel and we determine the modifications under which a similarity measure based on the notion of Hausdorff distance is also a Mercer's kernel. In both cases, we determine explicitly the mapping from input to feature space. The presented experimental results support the relevance of our analysis for developing effective trainable systems.     

On computation of the greatest common divisor of several polynomials over a finite field

We propose a probabilistic algorithm to reduce computing the greatest common divisor of m polynomials over a finite field (which requires computing m−1 pairwise greatest common divisors) to computing the greatest common divisor of two polynomials over the same field.     

Competing kinetic pathways in the bromine addition to allylic ethers in 1,2‐dichloroethane: Opposite temperature effects

The kinetics of the electrophilic bromination of three allylic ethers in a nonprotic solvent, 1,2‐dichloroethane, has been investigated. Two of them followed a prevalent second‐order pathway, while the third one exhibited a classical, clean third order. The second‐order pathway in the first two olefins is attributed to electrophilic assistance of the ethereal oxygen to the attacking bromine molecule. In the molecular bromination of 2,4‐cis‐dimethyl‐8‐oxabicyclo[3.2.1]‐6‐octen‐3‐cis‐ol, opposite temperature dependences were found for the two different kinetic pathways. An exoergonic process for the second‐order reaction was explained by the lesser stability of the bromiranium–bromide ionic intermediate, compared to the bromiranium–tribromide in the third‐order profile. © 2007 Wiley Periodicals, Inc. 39: 197–203, 2007